Showing papers on "Quantum state published in 2010"

Colloquium: Area laws for the entanglement entropy

Abstract: Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such ``area laws'' for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.

Quantum state tomography via compressed sensing.

Abstract: We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog^2d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.

Quantum Dots and Their Multimodal Applications: A Review

Abstract: Semiconducting quantum dots, whose particle sizes are in the nanometer range, have very unusual properties. The quantum dots have band gaps that depend in a complicated fashion upon a number of factors, described in the article. Processing-structure-properties-performance relationships are reviewed for compound semiconducting quantum dots. Various methods for synthesizing these quantum dots are discussed, as well as their resulting properties. Quantum states and confinement of their excitons may shift their optical absorption and emission energies. Such effects are important for tuning their luminescence stimulated by photons (photoluminescence) or electric field (electroluminescence). In this article, decoupling of quantum effects on excitation and emission are described, along with the use of quantum dots as sensitizers in phosphors. In addition, we reviewed the multimodal applications of quantum dots, including in electroluminescence device, solar cell and biological imaging.

Nonlinear atom interferometer surpasses classical precision limit

Abstract: Interference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements. Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose-Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states. Extending quantum interferometry to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the 'one-axis-twisting' scheme and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2 dB (refs 11-15). The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms.

Quantum-State Controlled Chemical Reactions of Ultracold Potassium-Rubidium Molecules

Abstract: How does a chemical reaction proceed at ultralow temperatures? Can simple quantum mechanical rules such as quantum statistics, single partial-wave scattering, and quantum threshold laws provide a clear understanding of the molecular reactivity under a vanishing collision energy? Starting with an optically trapped near-quantum-degenerate gas of polar 40K87Rb molecules prepared in their absolute ground state, we report experimental evidence for exothermic atom-exchange chemical reactions. When these fermionic molecules were prepared in a single quantum state at a temperature of a few hundred nanokelvin, we observed p-wave-dominated quantum threshold collisions arising from tunneling through an angular momentum barrier followed by a short-range chemical reaction with a probability near unity. When these molecules were prepared in two different internal states or when molecules and atoms were brought together, the reaction rates were enhanced by a factor of 10 to 100 as a result of s-wave scattering, which does not have a centrifugal barrier. The measured rates agree with predicted universal loss rates related to the two-body van der Waals length.

Unified View of Quantum and Classical Correlations

Abstract: We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to put all correlations on an equal footing. Entanglement and dissonance, whose definition is introduced here, jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states.

Universal Dynamical Decoupling of a Single Solid-State Spin from a Spin Bath

Abstract: Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We strongly suppressed the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence was preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement followed a general scaling with the number of decoupling pulses. No limit was observed for the decoupling action up to 136 pulses, for which the coherence time was enhanced more than 25 times compared to that obtained with spin echo. These results uncover a new regime for experimental quantum science and allow us to overcome a major hurdle for implementing quantum information protocols.

Observation of the fractional quantum Hall effect in graphene

Abstract: The fractional quantum Hall effect is a quintessential manifestation of the collective behaviour associated with strongly interacting charge carriers confined to two dimensions and subject to a strong magnetic field. It is predicted that the charge carriers present in graphene — an atomic layer of carbon that can be seen as the 'perfect' two-dimensional system — are subject to strong interactions. Nevertheless, the phenomenon had eluded experimental observation until now: in this issue two groups report fractional quantum Hall effect in suspended sheets of graphene, probed in a two-terminal measurement setup. The researchers also observe a magnetic-field-induced insulating state at low carrier density, which competes with the quantum Hall effect and limits its observation to the highest-quality samples only. These results pave the way for the study of the rich collective behaviour of Dirac fermions in graphene. The fractional quantum Hall effect (FQHE) is the quintessential collective quantum behaviour of charge carriers confined to two dimensions but it has not yet been observed in graphene, a material distinguished by the charge carriers' two-dimensional and relativistic character. Here, and in an accompanying paper, the FQHE is observed in graphene through the use of devices containing suspended graphene sheets; the results of these two papers open a door to the further elucidation of the complex physical properties of graphene. When electrons are confined in two dimensions and subject to strong magnetic fields, the Coulomb interactions between them can become very strong, leading to the formation of correlated states of matter, such as the fractional quantum Hall liquid1,2. In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. The experimental discovery of an anomalous integer quantum Hall effect in graphene has enabled the study of a correlated two-dimensional electronic system, in which the interacting electrons behave like massless chiral fermions3,4. However, owing to the prevailing disorder, graphene has so far exhibited only weak signatures of correlated electron phenomena5,6, despite intense experimental and theoretical efforts7,8,9,10,11,12,13,14. Here we report the observation of the fractional quantum Hall effect in ultraclean, suspended graphene. In addition, we show that at low carrier density graphene becomes an insulator with a magnetic-field-tunable energy gap. These newly discovered quantum states offer the opportunity to study correlated Dirac fermions in graphene in the presence of large magnetic fields.

Quantum computing with defects

Abstract: Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantum computer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV-1) center stands out for its robustness—its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV-1 center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors.

Efficient quantum state tomography

Abstract: Quantum state tomography--deducing quantum states from measured data--is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes unfeasible because the number of measurements and the amount of computation required to process them grows exponentially in the system size. Here, we present two tomography schemes that scale much more favourably than direct tomography with system size. One of them requires unitary operations on a constant number of subsystems, whereas the other requires only local measurements together with more elaborate post-processing. Both rely only on a linear number of experimental operations and post-processing that is polynomial in the system size. These schemes can be applied to a wide range of quantum states, in particular those that are well approximated by matrix product states. The accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.

Efficient quantum memory for light

Abstract: Storing and retrieving a quantum state of light on demand, without corrupting the information it carries, is an important challenge in the field of quantum information processing. Classical measurement and reconstruction strategies for storing light must necessarily destroy quantum information as a consequence of the Heisenberg uncertainty principle. There has been significant effort directed towards the development of devices-so-called quantum memories-capable of avoiding this penalty. So far, successful demonstrations of non-classical storage and on-demand recall have used atomic vapours and have been limited to low efficiencies, of less than 17 per cent, using weak quantum states with an average photon number of around one. Here we report a low-noise, highly efficient (up to 69 per cent) quantum memory for light that uses a solid-state medium. The device allows the storage and recall of light more faithfully than is possible using a classical memory, for weak coherent states at the single-photon level through to bright states of up to 500 photons. For input coherent states containing on average 30 photons or fewer, the performance exceeded the no-cloning limit. This guaranteed that more information about the inputs was retrieved from the memory than was left behind or destroyed, a feature that will provide security in communications applications.

Probabilistic theories with purification

Abstract: We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, that is, to the fact that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in quantum theory. Such an isomorphism allows one to prove most of the basic features of quantum theory, like, e.g., existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.

Almost all quantum states have nonclassical correlations

Abstract: Quantum discord quantifies nonclassical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension and have direct implications for quantum computation and for the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.

Dynamics of a quantum phase transition and relaxation to a steady state

Abstract: We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian. Accordingly, the review is divided into two parts. The first part revolves around a quantum version of the Kibble–Zurek mechanism including also phenomena that go beyond this simple paradigm. What they have in common is that excitation of a gapless many-body system scales with a power of the driving rate. The second part attempts a systematic presentation of recent results and conjectures on apparent relaxation of a pure state of an isolated quantum many-body system after its excitation by a sudden quench. This research is motivated in part by recent experimental developments in the physics of ultracold atoms with potential applications in the adiabatic quantum state preparation and quantum computation.

Theory of the thermal Hall effect in quantum magnets.

Abstract: We present a theory of the thermal Hall effect in insulating quantum magnets, where the heat current is totally carried by charge-neutral objects such as magnons and spinons. Two distinct types of thermal Hall responses are identified. For ordered magnets, the intrinsic thermal Hall effect for magnons arises when certain conditions are satisfied for the lattice geometry and the underlying magnetic order. The other type is allowed in a spin liquid which is a novel quantum state since there is no order even at zero temperature. For this case, the deconfined spinons contribute to the thermal Hall response due to Lorentz force. These results offer a clear experimental method to prove the existence of the deconfined spinons via a thermal transport phenomenon.

A derivation of quantum theory from physical requirements

Abstract: Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from five simple physical requirements, based on elementary assumptions about preparation, transformations and measurements. This is more similar to the usual formulation of special relativity, where two simple physical requirements -- the principles of relativity and light speed invariance -- are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three-dimensionality), and it suggests several natural possibilities to construct consistent modifications of quantum theory.

Measure for the non-Markovianity of quantum processes

Abstract: Recently, a measure for the non-Markovian behavior of quantum processes in open systems has been developed, which is based on the quantification of the flow of information between the open system and its environment [Phys. Rev. Lett. 103, 210401 (2009)]. The information flow is connected to the rate of change of the trace distance between quantum states, which can be interpreted in terms of the distinguishability of these states. Here, we elaborate the mathematical details of this theory, present applications to specific physical models, and discuss further theoretical and experimental implications as well as relations to alternative approaches proposed recently.

A trapped single ion inside a Bose-Einstein condensate.

Abstract: Improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of quantum-degenerate neutral atoms, and coherent light-matter interfaces have been built. Systems of single or a few trapped ions have been used to demonstrate universal quantum computing algorithms and to search for variations of fundamental constants in precision atomic clocks. Until now, atomic quantum gases and single trapped ions have been treated separately in experiments. Here we investigate whether they can be advantageously combined into one hybrid system, by exploring the immersion of a single trapped ion into a Bose-Einstein condensate of neutral atoms. We demonstrate independent control over the two components of the hybrid system, study the fundamental interaction processes and observe sympathetic cooling of the single ion by the condensate. Our experiment calls for further research into the possibility of using this technique for the continuous cooling of quantum computers. We also anticipate that it will lead to explorations of entanglement in hybrid quantum systems and to fundamental studies of the decoherence of a single, locally controlled impurity particle coupled to a quantum environment.

Complete hyperentangled-Bell-state analysis for quantum communication

Abstract: It is impossible to unambiguously distinguish the four Bell states in polarization, resorting to linear optical elements only. Recently, the hyperentangled Bell state, the simultaneous entanglement in more than one degree of freedom, has been used to assist in the complete Bell-state analysis of the four Bell states. However, if the additional degree of freedom is qubitlike, one can only distinguish 7 from the group of 16 states. Here we present a way to distinguish the hyperentangled Bell states completely with the help of cross-Kerr nonlinearity. Also, we discuss its application in the quantum teleportation of a particle in an unknown state in two different degrees of freedom and in the entanglement swapping of hyperentangled states. These applications will increase the channel capacity of long-distance quantum communication.

Experimental demonstration of phase-remapping attack in a practical quantum key distribution system

Abstract: Quantum key distribution (QKD) can, in principle, provide unconditional security based on the fundamental laws of physics. Unfortunately, a practical QKD system may contain overlooked imperfections and may thus violate some of the assumptions in the security proofs of QKD. It is important to explore these assumptions. One key assumption is that the sender (Alice) can prepare the required quantum states without errors. However, such an assumption may be violated in a practical QKD system. In this paper, we perform a proof-of-principle experiment to demonstrate a technically feasible 'intercept- and-resend' attack that exploits such a security loophole in a commercial 'plug & play' QKD system. The resulting quantum bit error rate is 19.7%, which is substantially lower than the well-known 25% error rate for an intercept-and-resend attack in BB84. The attack we utilize is the phase-remapping attack (Fung et al 2007 Phys. Rev. A 75 32314) proposed by our group.

States of an ensemble of two-level atoms with reduced quantum uncertainty.

Abstract: We generate entangled states of an ensemble of $5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ $^{87}\mathrm{Rb}$ atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise [up to 8.8(8) dB] with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.

Perfect, Efficent, State Transfer and its Application as a Constructive Tool

Abstract: We review the subject of perfect state transfer — how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.

One-step deterministic polarization-entanglement purification using spatial entanglement

Abstract: We present a one-step deterministic entanglement purification protocol with linear optics and postselection. Compared with the Simon-Pan protocol [C. Simon and J. W. Pan, Phys. Rev. Lett. 89, 257901 (2002)], this one-step protocol has some advantages. First, it can obtain a maximally entangled pair from each photon pair with only one step, instead of improving the fidelity of less-entangled photon pairs by performing the entanglement purification process repeatedly in other protocols. Second, it works in a deterministic way, not a probabilistic one, which greatly reduces the number of entanglement resources needed. Third, it does not require the polarization state be entangled; only spatial entanglement is needed. Moreover, it is feasible with current techniques [J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. Zellinger, Nature (London) 423, 417 (2003)]. All these advantages make this one-step protocol more convenient than others in quantum-communication applications.

Semiconductor Nanostructures: Quantum states and electronic transport

Abstract: 1. Introduction 2. Semiconductor Crystals 3. Band Structure 4. Envelope function and effective mass approximation 5. Material aspects of heterostructures, doping, surfaces, and gating 6. Fabrication of semiconductor nanostructures 7. Electrostatics of Semiconductor nanostructures 8. Quantum mechanics of semiconductor nanostructures 9. Two-dimensional electron gases in heterostructures 10. Diffusive classical transport in two-dimensional electron gases 11. Ballistic electron transport in quantum point contacts 12. Tunneling transport through potential barriers 13. Multiterminal systems 14. Interference effects in nanostructures 15. Diffusive quantum transport 16. Magnetotransport in two-dimensional systems 17. Interaction effects in diffusive two-dimensional systems 18. Quantum dots 19. Coupled quantum dots 20. Electronic noise in semiconductor nanostructures 21. The Fano effect 22. Measurements of the transmission phase 23. Controlled dephasing experiments 24. Quantum information processing

Quantum non-demolition detection of single microwave photons in a circuit

Abstract: Quantum non-demolition (QND) measurements interrogate a quantum state without disturbing it. A QND scheme that uses a superconducting circuit to investigate microwave photons trapped in a cavity is now shown. The measurement answers the question: are there exactly N photons in the cavity?

Unruh effect in quantum information beyond the single-mode approximation

Abstract: We address the validity of the single-mode approximation that is commonly invoked in the analysis of entanglement in noninertial frames and in other relativistic quantum-information scenarios. We show that the single-mode approximation is not valid for arbitrary states, finding corrections to previous studies beyond such approximations in the bosonic and fermionic cases. We also exhibit a class of wave packets for which the single-mode approximation is justified subject to the peaking constraints set by an appropriate Fourier transform.

Security proof for quantum key distribution using qudit systems

Abstract: We provide security bounds against coherent attacks for two families of quantum key distribution protocols that use $d$-dimensional quantum systems. In the asymptotic regime, both the secret key rate for fixed noise and the robustness to noise increase with $d$. The finite key corrections are found to be almost insensitive to $d\ensuremath{\lesssim}20$.

Quantum optomechanics—throwing a glance [Invited]

Abstract: Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling mechanical quantum states. We highlight some of the current challenges in the field by discussing two of our recent experiments.

Resonantly driven coherent oscillations in a solid-state quantum emitter

Abstract: Two experiments observe the so-called Mollow triplet in the emission spectrum of a quantum dot—originating from resonantly driving a dot transition—and demonstrate the potential of these systems to act as single-photon sources, and as a readout modality for electron-spin states. Single-quantum emitters emit only one photon at a time1,2, but the properties of the photon depend on how the emitter is excited3. Incoherent excitation is simple and broadly used with solid-state emitters such as quantum dots, but does not allow direct manipulation of the quantum state. Coherent, resonant excitation on the other hand is used in pump–probe techniques to examine the quantum state of the emitter4, but does not permit collection of the single-photon emission. Coherent control with simultaneous generation of photons has been an elusive goal in solid-state approaches, where, because of strong laser scattering at the detection wavelength, measurement of resonant emission has been limited to cross-polarized detection5 or Stokes-shift techniques6,7. Here we demonstrate that a semiconductor quantum dot in a microcavity can be resonantly driven and its single-photon emission extracted background free. Under strong continuous-wave excitation, the dot undergoes several Rabi oscillations before emitting, which are visible as oscillations in the second-order correlation function. The quantum-dot states are therefore ‘dressed’, resulting in a Mollow-triplet emission spectrum. Such coherent control will be necessary for future high-efficiency sources of indistinguishable single photons3,8, which can be used for quantum key distribution9 or through post-selection10 to generate entangled photon pairs11,12.

Experimental quantum-enhanced estimation of a lossy phase shift

Abstract: Evidence that appropriately engineered quantum states outperform both standard and N00N states in the precision of phase estimation — even in the presence of losses and decoherence — is presented. The results show that the strategy for realizing the quantum enhancement of metrology is quite distinct from protecting quantum information encoded in light.