Showing papers on "Quantum state published in 2013"
TL;DR: Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions as mentioned in this paper.
Abstract: Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on topological insulator materials with an emphasis on basic theory and materials properties. After presenting a historical perspective and basic theories of topological insulators, it discusses all the topological insulator materials discovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in which the author was involved. A summary is given for possible ways to confirm the topological nature in a candidate material. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulating samples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transport properties. In particular, the Dirac fermion physics and the resulting peculiar quantum oscillation patterns are discussed in detail. It is emphasized that proper analyses of quantum oscillations make it possible to unambiguously identify surface Dirac fermions through transport measurements. The prospects of topological insulator materials for elucidating novel quantum phenomena that await discovery conclude the review.
1,065 citations
TL;DR: Using time- and angle-resolved photoemission spectroscopy, it is shown that an intense ultrashort midinfrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands.
Abstract: The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum Hall state. Using time- and angle-resolved photoemission spectroscopy, we show that an intense ultrashort midinfrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands. These photon-dressed surface bands exhibit polarization-dependent band gaps at avoided crossings. Circularly polarized photons induce an additional gap at the Dirac point, which is a signature of broken time-reversal symmetry on the surface. These observations establish the Floquet-Bloch bands in solids and pave the way for optical manipulation of topological quantum states of matter.
859 citations
TL;DR: It is shown that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sub linear amount of classical communication required for entanglement dilution.
Abstract: The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here, we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.
632 citations
TL;DR: Experimental control of quantum systems has been pursued widely since the invention of quantum mechanics as mentioned in this paper, with many of these works focusing on the control of internal and external states of trapped atomic ions, such as Bose-Einstein condensation.
Abstract: Experimental control of quantum systems has been pursued widely since the invention of quantum mechanics In the first part of the 20th century, atomic physics helped provide a test bed for quantum mechanics through studies of atoms’ internal energy differences and their interaction with radiation The advent of spectrally pure, tunable radiation sources such as microwave oscillators and lasers dramatically improved these studies by enabling the coherent control of atoms’ internal states to deterministically prepare superposition states, as, for example, in the Ramsey method (Ramsey, 1990) More recently this control has been extended to the external (motional) states of atoms Laser cooling and other refrigeration techniques have provided the initial states for a number of interesting studies, such as Bose-Einstein condensation Similarly, control of the quantum states of artificial atoms in the context of condensed-matter systems is achieved in many laboratories throughout theworld To give proper recognition to all of these works would be a daunting task; therefore, I will restrict these notes to experiments on quantum control of internal and external states of trapped atomic ions The precise manipulation of any system requires lownoise controls and isolation of the system from its environment Of course the controls can be regarded as part of the environment, so we mean that the system must be isolated from the uncontrolled or noisy parts of the environment A simple example of quantum control comes from nuclear magnetic resonance, where the spins of a macroscopic ensemble of protons in the state j #i (spin antiparallel to an applied magnetic field) can be deterministically placed in a superposition state j #i þ j "i (j j2 þ j j2 1⁄4 1) by application of a resonant rf field for a specified duration Although the ensemble is macroscopic, in this example each spin is independent of the others and behaves as an individual quantum system But already in 1935, Erwin Schrodinger (Schrodinger, 1935) realized that, in principle, quantum mechanics should apply to a macroscopic system in a more complex way, which could then lead to bizarre consequences In his specific example, the system is composed of a single radioactive particle and a cat placed together with a mechanism such that if the particle decays, poison is released, which kills the cat Quantum mechanically we represent the quantum states of the radioactive particle as undecayed 1⁄4 j "i or decayed 1⁄4 j #i, and live and dead states of the cat as jLi and jDi If the system is initialized in the state represented by the wave function j "ijLi, then after a duration equal to the half life of the particle, quantum mechanics says the system evolves to a superposition state where the cat is alive and dead simultaneously, expressed by the superposition wave function
407 citations
TL;DR: In this paper, the authors established a quantum measure of classicality in the form of the occupation number, N, of gravitons in a gravitational field and showed that among all possible sources of a given physical length, N is maximized by the black hole and coincides with its entropy.
Abstract: We establish a quantum measure of classicality in the form of the occupation number, N, of gravitons in a gravitational field. This allows us to view classical background geometries as quantum Bose-condensates with large occupation numbers of soft gravitons. We show that among all possible sources of a given physical length, N is maximized by the black hole and coincides with its entropy. The emerging quantum mechanical picture of a black hole is surprisingly simple and fully parameterized by N. The black hole is a leaky bound-state in form of a cold Bose-condensate of N weakly-interacting soft gravitons of wave-length N**(1/2) times the Planck length and of quantum interaction strength 1/N. Such a bound-state exists for an arbitrary N. This picture provides a simple quantum description of the phenomena of Hawking radiation, Bekenstein entropy as well as of non-Wilsonian UV-self-completion of Einstein gravity. We show that Hawking radiation is nothing but a quantum depletion of the graviton Bose-condensate, which despite the zero temperature of the condensate produces a thermal spectrum of temperature T = 1/(N**(1/2)). The Bekenstein entropy originates from the exponentially growing with N number of quantum states. Finally, our quantum picture allows to understand classicalization of deep-UV gravitational scattering as 2 -> N transition. We point out some fundamental similarities between the black holes and solitons, such as a t'Hooft-Polyakov monopole. Both objects represent Bose-condensates of N soft bosons of wavelength N**(1/2) and interaction strength 1/N. In short, the semi-classical black hole physics is 1/N-coupled large-N quantum physics.
391 citations
TL;DR: It is demonstrated that the state of an itinerant microwave field can be coherently transferred into, stored in and retrieved from a mechanical oscillator with amplitudes at the single-quantum level.
Abstract: Macroscopic mechanical oscillators have been coaxed into a regime of quantum behaviour by direct refrigeration or a combination of refrigeration and laser-like cooling. This result supports the idea that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits, either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems. As yet, the transfer of an itinerant state or a propagating mode of a microwave field to and from a storage medium has not been demonstrated, owing to the inability to turn on and off the interaction between the microwave field and the medium sufficiently quickly. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in and retrieved from a mechanical oscillator with amplitudes at the single-quantum level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store quantum information and enable its transfer between otherwise incompatible systems.
382 citations
TL;DR: In this paper, it was shown that closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate, even though prepared with macroscopic amounts of energy above their ground states.
Abstract: Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate, even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can order, in that individual many-body eigenstates can break symmetries or display topological order in the infinite-volume limit. Indeed, isolated localized quantum systems can order even at energy densities where the corresponding thermally equilibrated system is disordered, i.e., localization protects order. In addition, localized systems can move between ordered and disordered localized phases via nonthermodynamic transitions in the properties of the many-body eigenstates. We give evidence that such transitions may proceed via localized critical points. We note that localization provides protection against decoherence that may allow experimental manipulation of macroscopic quantum states. We also identify a ``spectral transition'' involving a sharp change in the spectral statistics of the many-body Hamiltonian.
359 citations
TL;DR: In this article, it is shown how to view the Born rule as a normative rule in addition to usual Dutch-book coherence, and the extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.
Abstract: In the quantum-Bayesian interpretation of quantum theory (or QBism), the Born rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, the argument is given that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, it is shown how to view the Born rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is exemplified by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete measurement. The extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.
331 citations
TL;DR: In this paper, the authors develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment, and they also show that remote steering of quantum states can be described within their formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences.
Abstract: Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment. In addition, concepts that are distinct in the conventional formalism become unified: Channels, sets of states, and positive operator valued measures are all seen to be instances of conditional states; the action of a channel on a state, ensemble averaging, the Born rule, the composition of channels, and nonselective state-update rules are all seen to be instances of belief propagation. Using a quantum generalization of Bayes' theorem and the associated notion of Bayesian conditioning, we also show that the remote steering of quantum states can be described within our formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences. Finally, we show that previous arguments for interpreting the projection postulate as a quantum generalization of Bayesian conditioning are based on a misleading analogy and that it is best understood as a combination of belief propagation (corresponding to the nonselective state-update map) and conditioning on the measurement outcome.
328 citations
TL;DR: A brief review of the basic physics of quantum optomechanics and an overview of some of its recent developments and current areas of focus can be found in this article, along with an outlook that concentrates largely on the functionalization of quantum Optomechanical systems and their promise in metrology applications.
Abstract: This paper gives a brief review of the basic physics of quantum optomechanics and provides an overview of some of its recent developments and current areas of focus. It first outlines the basic theory of cavity optomechanical cooling and gives a brief status report of the experimental state-of-the-art. It then turns to the deep quantum regime of operation of optomechanical oscillators and covers selected aspects of quantum state preparation, control and characterization, including mechanical squeezing and pulsed optomechanics. This is followed by a discussion of the “bottom-up” approach that exploits ultracold atomic samples instead of nanoscale systems. It concludes with an outlook that concentrates largely on the functionalization of quantum optomechanical systems and their promise in metrology applications.
310 citations
TL;DR: Through the collective read-out of these pseudospin rotations it is shown that the microwave field modifies the long-range interactions between polaritons.
Abstract: We use a microwave field to control the quantum state of optical photons stored in a cold atomic cloud. The photons are stored in highly excited collective states (Rydberg polaritons) enabling both fast qubit rotations and control of photon-photon interactions. Through the collective read-out of these pseudospin rotations it is shown that the microwave field modifies the long-range interactions between polaritons. This technique provides a powerful interface between the microwave and optical domains, with applications in quantum simulations of spin liquids, quantum metrology and quantum networks.
TL;DR: Through entanglement maps, this work reveals rich information contained in the wavefunctions on bonding changes in the cycle, and suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed.
Abstract: It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn_4CaO_5 cluster of photosystem II, with more than 1 × 10^(18) quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.
TL;DR: In this article, the authors demonstrated an optical realization of self-trapping and Josephson oscillations using polariton condensates in overlapping microcavities, and demonstrated that such effects can be observed in optical systems.
Abstract: The Josephson effects that arise when two quantum states are coupled through a barrier are difficult to observe in optical systems because photon–photon interactions are so weak. Researchers have now demonstrated an optical realization of two such phenomena—macroscopic self-trapping and Josephson oscillations—using polariton condensates in overlapping microcavities.
TL;DR: Analytical and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code is reported and it is proved that its memory time is at least L(cβ), where L is the lattice size, β is the inverse temperature of the bath, and c>0 is a constant coefficient.
Abstract: A big open question in the quantum information theory concerns the feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction, if the memory is in contact with a cold enough thermal bath. Here we report analytic and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code. We prove that its memory time is at least L^(cβ), where L is the lattice size, β is the inverse temperature of the bath, and c>0 is a constant coefficient. However, this bound applies only if the lattice size L does not exceed a critical value which grows exponentially with β. In that sense, the model can be called a partially self-correcting memory. We also report a Monte Carlo simulation indicating that our analytic bounds on the memory time are tight up to constant coefficients. To model the readout step we introduce a new decoding algorithm, which can be implemented efficiently for any topological stabilizer code. A longer version of this work can be found in Bravyi and Haah, arXiv:1112.3252.
TL;DR: In this article, the authors review a set of techniques of quantum measurement theory that are often used to analyse quantum optomechanical systems, including quantum entanglement, quantum teleportation and quantum Zeno effect.
Abstract: Rapid experimental progress has recently allowed the use of light to prepare macroscopic mechanical objects into nearly pure quantum states. This research field of quantum optomechanics opens new doors towards testing quantum mechanics, and possibly other laws of physics, in new regimes. In the first part of this article, I will review a set of techniques of quantum measurement theory that are often used to analyse quantum optomechanical systems. Some of these techniques were originally designed to analyse how a classical driving force passes through a quantum system, and can eventually be detected with an optimal signal-to-noise ratio—while others focus more on the quantum-state evolution of a mechanical object under continuous monitoring. In the second part of this article, I will review a set of experimental concepts that will demonstrate quantum mechanical behaviour of macroscopic objects—quantum entanglement, quantum teleportation and the quantum Zeno effect. Taking the interplay between gravity and quantum mechanics as an example, I will review a set of speculations on how quantum mechanics can be modified for macroscopic objects, and how these speculations—and their generalizations—might be tested by optomechanics.
TL;DR: In this paper, a spin-mechanical coupling with a built-in nitrogen-vacancy center inside the nanodiamond was proposed to generate large quantum superposition states and arbitrary Fock states.
Abstract: We propose a method to generate and detect large quantum superposition states and arbitrary Fock states for the oscillational mode of an optically levitated nanocrystal diamond. The nonlinear interaction required for the generation of non-Gaussian quantum states is enabled through the spin-mechanical coupling with a built-in nitrogen-vacancy center inside the nanodiamond. The proposed method allows the generation of large superpositions of nanoparticles with millions of atoms and the observation of the associated spatial quantum interference under reasonable experimental conditions.
TL;DR: An experimental system capable of detecting a single photon without destroying it is described and the large single-photon nonlinearity of the experiment should enable the development of photonic quantum gates and the preparation of exotic quantum states of light.
Abstract: All optical detectors to date annihilate photons upon detection, thus excluding repeated measurements. Here, we demonstrate a robust photon detection scheme that does not rely on absorption. Instead, an incoming photon is reflected from an optical resonator containing a single atom prepared in a superposition of two states. The reflection toggles the superposition phase, which is then measured to trace the photon. Characterizing the device with faint laser pulses, a single-photon detection efficiency of 74% and a survival probability of 66% are achieved. The efficiency can be further increased by observing the photon repeatedly. The large single-photon nonlinearity of the experiment should enable the development of photonic quantum gates and the preparation of exotic quantum states of light.
TL;DR: A nondestructive imaging method is demonstrated to monitor the migration of electronic excitations with high time and spatial resolution, using electromagnetically induced transparency on a background gas acting as an amplifier to determine the many-body dynamics of the energy transport.
Abstract: Electronically highly excited (Rydberg) atoms experience quantum state–changing interactions similar to Forster processes found in complex molecules, offering a model system to study the nature of dipole-mediated energy transport under the influence of a controlled environment. We demonstrate a nondestructive imaging method to monitor the migration of electronic excitations with high time and spatial resolution, using electromagnetically induced transparency on a background gas acting as an amplifier. The continuous spatial projection of the electronic quantum state under observation determines the many-body dynamics of the energy transport.
TL;DR: In this article, the authors develop a resource theory analogous to the theory of entanglement for resources for stabilizer codes and introduce two quantitative measures -monotones - for the amount of non-stabilizer resource.
Abstract: Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, for resources for stabilizer codes. We introduce two quantitative measures - monotones - for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behaviour.
TL;DR: The TPQ formulation of statistical mechanics is established, according to which all quantities of statistical-mechanical interest are obtained from a single realization of any TPQ state, and it is shown that it has great advantages in practical applications.
Abstract: Every equilibrium state can be represented by a typical pure quantum state, the thermal pure quantum (TPQ) state. I particularly focus on the TPQ state which corresponds to the canonical ensemble and show that any physical quantities of statistical-mechanical interest are obtained from a single realization of the TPQ state. With these findings, I formulate statistical mechanics based on the TPQ state.
TL;DR: In this article, the authors studied the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain and proposed a criterion for the identification of the many-body localization transition based on the distribution of the wave function coefficients, a standard observable in modern studies of Anderson localization.
Abstract: We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non-ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be allowed by the conservation of extensive observables. By the anomalous scaling of the participation ratios with system size we are led to consider the distribution of the wave function coefficients, a standard observable in modern studies of Anderson localization. We finally present a criterion for the identification of the ergodicity-breaking (many-body localization) transition based on these distributions which is quite robust and well suited for numerical investigations of a broad class of problems.
TL;DR: The experimental observation of three-photon interference in an integrated three-port directional coupler realized by ultrafast laser writing is reported, which allows for bosonic coalescence of three photons and opens new important perspectives in many areas of quantum information.
Abstract: The main features of quantum mechanics reside in interference deriving from the superposition of different quantum states. While current quantum optical technology enables two-photon interference both in bulk and integrated systems, simultaneous interference of more than two particles, leading to richer quantum phenomena, is still a challenging task. Here we report the experimental observation of three-photon interference in an integrated three-port directional coupler realized by ultrafast laser writing. By exploiting the capability of this technique to produce three-dimensional structures, we realized and tested in the quantum regime a three-port beam splitter, namely a tritter, which allowed us to observe bosonic coalescence of three photons. These results open new important perspectives in many areas of quantum information, such as fundamental tests of quantum mechanics with increasing number of photons, quantum state engineering, quantum sensing and quantum simulation. For the development and application of quantum technologies, devices capable of implementing more than two-photon processes are vital. Towards this aim, Spagnolo et al.build a three-port beam splitter and demonstrate mutual interference between the three photons.
TL;DR: In this paper, it was shown that if the prior information restricts the possible states to a set of lower dimensionality, then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters.
Abstract: We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify an unknown quantum state which is constrained by prior information? We show that if the prior information restricts the possible states to a set of lower dimensionality, then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters needed to characterize the set of all states. Conversely, we show that almost every measurement becomes informationally complete with respect to the constrained set if the number of outcomes exceeds twice the Minkowski dimension of the set. We apply the obtained results to determine the minimal number of outcomes of measurements which are informationally complete with respect to states with rank constraints. In particular, we show that the minimal number of measurement outcomes (POVM elements) necessary to identify all pure states in a d-dimensional Hilbert space is 4d−3−c(d) α(d) for some \({c(d)\in[1,2]}\) and α(d) being the number of ones appearing in the binary expansion of (d−1).
TL;DR: In this paper, a method for analyzing the past of a quantum particle according to the weak trace it leaves is proposed, which can be observed via measurements performed on an ensemble of identically pre- and postselected particles.
Abstract: Although there is no consensus regarding the ``reality'' of the past of a quantum particle, in situations where there is only one trajectory with a nonvanishing quantum wave of the particle between its emission and detection points, it seems ``safe'' to associate the past of the particle with this trajectory. A method for analyzing the past of a quantum particle according to the weak trace it leaves is proposed. Such a trace can be observed via measurements performed on an ensemble of identically pre- and postselected particles. Examples in which this method contradicts the above common sense description of the past of the particle are presented. It is argued that it is possible to describe the past of a quantum particle, but the naive approach has to be replaced by both forward- and backward-evolving quantum states.
TL;DR: In this article, the authors introduce two alternative definitions of $n$-way nonlocality, which are better motivated both from the point of view of the study of nature, and from quantum information theory.
Abstract: In a multipartite setting, it is possible to distinguish quantum states that are genuinely $n$-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely $n$-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of $n$-way nonlocality, which we argue are better motivated both from the point of view of the study of nature, and from the point of view of quantum information theory. We show that these definitions are strictly weaker than Svetlichny's, and introduce a series of suitable Bell-type inequalities for the detection of three-way nonlocality. Numerical evidence suggests that all three-way entangled pure quantum states can produce three-way nonlocal correlations.
TL;DR: In this article, the Hermiticity condition in quantum mechanics required for the characterisation of physical observables and generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and their eigenstates are complete.
Abstract: The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert space dimensionality is finite. Specifically, characterisations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.
TL;DR: This work shows that in the case of pure, multiparticle quantum states, features of the global entanglement can already be extracted from local information alone and gives rise to local witnesses for global pure-state entanglements and can be generalized to states affected by low levels of noise.
Abstract: Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure, multiparticle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating any given class of entanglement with an entanglement polytope-a geometric object that characterizes the single-particle states compatible with that class. Our results, applicable to systems of arbitrary size and statistics, give rise to local witnesses for global pure-state entanglement and can be generalized to states affected by low levels of noise.
TL;DR: In this article, a class of multiqubit quantum states which generalize graph states was introduced, which correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered.
Abstract: We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalized stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch–Jozsa's and Grover's.
TL;DR: This work proposes another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector, and the security of the protocol is based on the no-signaling principle, which is more fundamental than quantum physics.
Abstract: Blind quantum computation is a new secure quantum computing protocol which enables Alice (who does not have sufficient quantum technology) to delegate her quantum computation to Bob (who has a full-fledged quantum computer) in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. In previous protocols, Alice needs to have a device which generates quantum states, such as single-photon states. Here we propose another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector. In several experimental setups, such as optical systems, the measurement of a state is much easier than the generation of a single-qubit state. Therefore our protocols ease Alice's burden. Furthermore, the security of our protocol is based on the no-signaling principle, which is more fundamental than quantum physics. Finally, our protocols are device independent in the sense that Alice does not need to trust her measurement device in order to guarantee the security.
TL;DR: In this article, the authors demonstrate the deterministic continuous-variable teleportation between two atomic ensembles at room temperature, which makes it possible to teleport time-evolving quantum states from one ensemble to the other.
Abstract: An experiment now demonstrates the deterministic continuous-variable teleportation between two atomic ensembles at room temperature. This protocol makes it possible to teleport time-evolving quantum states from one ensemble to the other.