Showing papers on "Quantum state published in 2002"
Book•
29 Aug 2002
TL;DR: Probability in classical and quantum physics has been studied in this article, where classical probability theory and stochastic processes have been applied to quantum optical systems and non-Markovian dynamics in physical systems.
Abstract: PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3. Quantum Master Equations 4. Decoherence PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE 5. Probability distributions on Hilbert space 6. Stochastic dynamics in Hilbert space 7. The stochastic simulation method 8. Applications to quantum optical systems PART 4: NON-MARKOVIAN QUANTUM PROCESSES 9. Projection operator techniques 10. Non-Markovian dynamics in physical systems PART 5: RELATIVISTIC QUANTUM PROCESSES 11. Measurements in relativistic quantum mechanics 12. Open quantum electrodynamics
6,325 citations
01 Mar 2002
TL;DR: In this article, an implementation of Grover's algorithm that uses molecular magnets was proposed, which can be used to build dense and efficient memory devices based on the Grover algorithm, in which one single crystal can serve as a storage unit of a dynamic random access memory device.
Abstract: Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers1 and in searching a database2 by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system3, the superposition of single-particle quantum states is sufficient for Grover's algorithm4. Recently, the latter has been successfully implemented5 using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets6,7,8,9,10, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.
1,942 citations
TL;DR: An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail in this article, based on the control of photon propagation in coherently driven three-level atomic media.
Abstract: An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven three-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in electromagnetically induced transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.
626 citations
TL;DR: In this paper, a projective symmetry group was introduced to characterize quantum orders and construct hundreds of symmetric spin liquids, which have SU(2), U(1), or Z{Z}_{2}$ gauge structures at low energies.
Abstract: A concept---quantum order---is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize the universality classes of quantum states (described by complex ground-state wave functions) are much richer than classical orders that characterize the universality classes of finite-temperature classical states (described by positive probability distribution functions). Landau's theory for orders and phase transitions does not apply to quantum orders since they cannot be described by broken symmetries and the associated order parameters. We introduced a mathematical object---projective symmetry group---to characterize quantum orders. With the help of quantum orders and projective symmetry groups, we construct hundreds of symmetric spin liquids, which have SU(2), U(1), or ${Z}_{2}$ gauge structures at low energies. We found that various spin liquids can be divided into four classes: (a) Rigid spin liquid---spinons (and all other excitations) are fully gapped and may have bosonic, fermionic, or fractional statistics. (b) Fermi spin liquid---spinons are gapless and are described by a Fermi liquid theory. (c) Algebraic spin liquid---spinons are gapless, but they are not described by free fermionic-bosonic quasiparticles. (d) Bose spin liquid---low-lying gapless excitations are described by a free-boson theory. The stability of those spin liquids is discussed in detail. We find that stable two-dimensional spin liquids exist in the first three classes (a)--(c). Those stable spin liquids occupy a finite region in phase space and represent quantum phases. Remarkably, some of the stable quantum phases support gapless excitations even without any spontaneous symmetry breaking. In particular, the gapless excitations in algebraic spin liquids interact down to zero energy and the interaction does not open any energy gap. We propose that it is the quantum orders (instead of symmetries) that protect the gapless excitations and make algebraic spin liquids and Fermi spin liquids stable. Since high-${T}_{c}$ superconductors are likely to be described by a gapless spin liquid, the quantum orders and their projective symmetry group descriptions lay the foundation for a spin liquid approach to high-${T}_{c}$ superconductors.
588 citations
TL;DR: The generation and observation of coherent temporal oscillations between the macroscopic quantum states of a Josephson tunnel junction are reported by applying microwaves with frequencies close to the level separation.
Abstract: We report the generation and observation of coherent temporal oscillations between the macroscopic quantum states of a Josephson tunnel junction by applying microwaves with frequencies close to the level separation. Coherent temporal oscillations of excited state populations were observed by monitoring the junction's tunneling probability as a function of time. From the data, the lower limit of phase decoherence time was estimated to be about 5 microseconds.
539 citations
TL;DR: Condensates have become an ultralow-temperature laboratory for atom optics, collisional physics and many-body physics, encompassing phonons, superfluidity, quantized vortices, Josephson junctions and quantum phase transitions.
Abstract: The early experiments on Bose-Einstein condensation in dilute atomic gases accomplished three long-standing goals. First, cooling of neutral atoms into their motional ground state, thus subjecting them to ultimate control, limited only by Heisenberg's uncertainty relation. Second, creation of a coherent sample of atoms, in which all occupy the same quantum state, and the realization of atom lasers - devices that output coherent matter waves. And third, creation of a gaseous quantum fluid, with properties that are different from the quantum liquids helium-3 and helium-4. The field of Bose-Einstein condensation of atomic gases has continued to progress rapidly, driven by the combination of new experimental techniques and theoretical advances. The family of quantum-degenerate gases has grown, and now includes metastable and fermionic atoms. Condensates have become an ultralow-temperature laboratory for atom optics, collisional physics and many-body physics, encompassing phonons, superfluidity, quantized vortices, Josephson junctions and quantum phase transitions.
493 citations
TL;DR: The quantum dynamics of a micromechanical resonator capacitively coupled to a Cooper-pair box is analyzed and the resonator can be driven into a superposition of spatially separated states.
Abstract: We analyze the quantum dynamics of a micromechanical resonator capacitively coupled to a Cooper-pair box With appropriate quantum state control of the Cooper box, the resonator can be driven into a superposition of spatially separated states The Cooper box can also be used to probe the decay of the resonator superposition state due to environmental decoherence
439 citations
01 Jan 2002
TL;DR: In this paper, the density matrices and Wigner functions for various quantum states of motion of a harmonically bound ion were reconstructed using coherent displacements of different amplitudes and phases.
Abstract: We reconstruct the density matrices and Wigner functions for various quantum states of motion of a harmonically bound ${}^{9}{\mathrm{Be}}^{+}$ ion. We apply coherent displacements of different amplitudes and phases to the input state and measure the number state populations. Using novel reconstruction schemes we independently determine both the density matrix in the number state basis and the Wigner function. These reconstructions are sensitive indicators of decoherence in the system.
387 citations
TL;DR: In this article, the decoherence mechanisms likely to dominate in a biological setting were examined, and it was shown that a hybrid of the Penrose-Hameroff orchestrated objective reduction (orch. OR) model with a soliton in superposition along the microtubule can significantly increase the quantum coherence of microtubules.
Abstract: The Penrose-Hameroff orchestrated objective reduction ~orch. OR! model assigns a cognitive role to quantum computations in microtubules within the neurons of the brain. Despite an apparently ‘‘warm, wet, and noisy’’ intracellular milieu, the proposal suggests that microtubules avoid environmental decoherence long enough to reach threshold for ‘‘self-collapse’’ ~objective reduction! by a quantum gravity mechanism put forth by Penrose. The model has been criticized as regards the issue of environmental decoherence, and a recent report by Tegmark finds that microtubules can maintain quantum coherence for only 10 213 s, far too short to be neurophysiologically relevant. Here, we critically examine the decoherence mechanisms likely to dominate in a biological setting and find that ~1! Tegmark’s commentary is not aimed at an existing model in the literature but rather at a hybrid that replaces the superposed protein conformations of the orch. OR theory with a soliton in superposition along the microtubule; ~2! recalculation after correcting for differences between the model on which Tegmark bases his calculations and the orch. OR model ~superposition separation, charge vs dipole, dielectric constant! lengthens the decoherence time to 10 25 ‐10 24 s; ~3! decoherence times on this order invalidate the assumptions of the derivation and determine the approximation regime considered by Tegmark to be inappropriate to the orch. OR superposition; ~4! Tegmark’s formulation yields decoherence times that increase with temperature contrary to well-established physical intuitions and the observed behavior of quantum coherent states; ~5! incoherent metabolic energy supplied to the collective dynamics ordering water in the vicinity of microtubules at a rate exceeding that of decoherence can counter decoherence effects ~in the same way that lasers avoid decoherence at room temperature!; ~6! microtubules are surrounded by a Debye layer of counterions, which can screen thermal fluctuations, and by an actin gel that might enhance the ordering of water in bundles of microtubules, further increasing the decoherence-free zone by an order of magnitude and, if the dependence on the distance between environmental ion and superposed state is accurately reflected in Tegmark’s calculation, extending decoherence times by three orders of magnitude; ~7! topological quantum computation in microtubules may be error correcting, resistant to decoherence; and ~8! the decohering effect of radiative scatterers on microtubule quantum states is negligible. These considerations bring microtubule decoherence into a regime in which quantum gravity could interact with neurophysiology.
373 citations
TL;DR: This work studies optimal eavesdropping in quantum cryptography with three-dimensional systems, and shows that this scheme is more secure against symmetric attacks than protocols using two-dimensional states.
Abstract: We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure against symmetric attacks than protocols using two-dimensional states. We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.
370 citations
TL;DR: The Fock space of a system of indistinguishable particles is isomorphic (in a nonunique way) to the state space of composite, i.e., many modes, quantum systems as mentioned in this paper.
Abstract: The Fock space of a system of indistinguishable particles is isomorphic (in a nonunique way) to the state space of a composite, i.e., many modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems. We exemplify the use of this notion---central in quantum information---by studying some, e.g., Hubbard, lattice fermionic models relevant to condensed matter physics.
TL;DR: In this paper, the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles is introduced and a correlation measure for indistinguishable particles is provided.
TL;DR: In this article, the authors extend the tomographic reconstruction technique to two new regimes: one-and two-qutrit systems, and show how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qubit systems.
Abstract: Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally, orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First, we show how nonorthogonal measurements allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qutrit systems.
TL;DR: For finite-dimensional bipartite quantum systems, the exact size of the largest balls, in spectral ρ-norms, in the sense that their purity is not too large, has been shown in this paper.
Abstract: For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral ${l}_{p}$ norms for $1l~pl~\ensuremath{\infty},$ of separable (unentangled) matrices around the identity matrix. This implies a simple and intuitively meaningful geometrical sufficient condition for separability of bipartite density matrices: that their purity $\mathrm{tr}{\ensuremath{\rho}}^{2}$ not be too large. Theoretical and experimental applications of these results include algorithmic problems such as computing whether or not a state is entangled, and practical ones such as obtaining information about the existence or nature of entanglement in states reached by nuclear magnetic resonance quantum computation implementations or other experimental situations.
TL;DR: A fundamental asymmetry to nonlocality is revealed, which is the origin of "nonlocality without entanglement," and a very simple proof of this phenomenon is presented.
Abstract: Entanglement is a useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and what is not locally possible. We focus on orthogonal states, which can always be globally distinguished. We establish the necessary and sufficient conditions for a general set of $2\ifmmode\times\else\texttimes\fi{}2$ quantum states to be locally distinguishable, and for a general set of $2\ifmmode\times\else\texttimes\fi{}n$ quantum states to be distinguished given an initial measurement of the qubit. These results reveal a fundamental asymmetry to nonlocality, which is the origin of ``nonlocality without entanglement,'' and we present a very simple proof of this phenomenon.
TL;DR: It is demonstrated how molecular quantum states of coupled semiconductor quantum dots are coherently probed and manipulated in transport experiments by weakly probing the quantum system through parallel contacts to its constituting quantum dots.
Abstract: We demonstrate how molecular quantum states of coupled semiconductor quantum dots are coherently probed and manipulated in transport experiments. The applied method probes quantum states by the virtual cotunneling of two electrons and hence resolves the sequences of molecular states simultaneously. This result is achieved by weakly probing the quantum system through parallel contacts to its constituting quantum dots. The overlap of the dots' wave functions and, in turn, the splitting of molecular states are adjusted by the direct influence of coupling electrodes.
TL;DR: The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schrödinger equation, valid at arbitrary temperature and damping strength, and exemplified by an application to the dissipative two-state system.
Abstract: The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schrodinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born-Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.
Posted Content•
TL;DR: In this paper, the authors studied the authentication of messages composed of quantum states and gave a formal definition of authentication in the quantum setting, and proposed a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s.
Abstract: Authentication is a well-studied area of classical cryptography: a sender A and a receiver B sharing a classical secret key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In this paper we study the authentication of messages composed of quantum states. We give a formal definition of authentication in the quantum setting. Assuming A and B have access to an insecure quantum channel and share a secret, classical random key, we provide a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s. The scheme requires a secret key of size 2m+O(s). To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs. It has long been known that learning information about a general quantum state will necessarily disturb it. We refine this result to show that such a disturbance can be done with few side effects, allowing it to circumvent cryptographic protections. Consequently, any scheme to authenticate quantum messages must also encrypt them. In contrast, no such constraint exists classically. This reasoning has two important consequences: It allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. Moreover, we use it to show that digitally signing quantum states is impossible.
TL;DR: Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, the authors compute compact representations of the spin-spin correlation functions of the XXZ-1 2 Heisenberg chain in a magnetic field.
TL;DR: It is shown that new quantum states that "compete" to be the most probable state appear, in clear contrast with the commutative case, in the noncommutative quantum cosmology model.
Abstract: We propose a model for noncommutative quantum cosmology by means of a deformation of minisuperspace For the Kantowski-Sachs metric we are able to find the exact wave function We construct wave packets and show that new quantum states that "compete" to be the most probable state appear, in clear contrast with the commutative case A tunneling process could be possible among these states
TL;DR: In this paper, it was shown that, except for the thermal vacuum, free scalar fields in de Sitter space have a one-parameter family of states invariant under the standard thermal vacuum.
Abstract: Free scalar fields in de Sitter space have a one-parameter family of states invariant under the de Sitter group, including the standard thermal vacuum. We show that, except for the thermal vacuum, these states are unphysical when gravitational interactions are included. We apply these observations to the quantum state of the inflaton, and find that at best, dramatic fine tuning is required for states other than the thermal vacuum to lead to observable features in the CMBR anisotropy.
TL;DR: A necessary and sufficient hierarchy of conditions is derived that is completely equivalent to the failure of the Glauber-Sudarshan P function to be a probability density.
Abstract: A necessary and sufficient hierarchy of conditions is derived that is completely equivalent to the failure of the Glauber-Sudarshan P function to be a probability density. The conditions are formulated in terms of experimentally accessible characteristic functions of quadratures.
TL;DR: It is shown that Otto cycle engine performance can be improved beyond that of the "ideal" Otto heat engine and a new kind of lasing without initial inversion is demonstrated.
Abstract: By using a laser and maser in tandem, it is possible to obtain laser action in the hot exhaust gases of a heat engine. Such a “quantum afterburner” involves the internal quantum states of the working molecules as well as the techniques of cavity quantum electrodynamics and is therefore in the domain of quantum thermodynamics. It is shown that Otto cycle engine performance can be improved beyond that of the “ideal” Otto heat engine. Furthermore, the present work demonstrates a new kind of lasing without initial inversion.
TL;DR: A statistical multistream description of quantum plasmas is formulated, and a Landau-like damping of plane wave perturbations occurs due to the broadening of the background Wigner function that arises as a consequence of statistical variations of the wave function phase.
Abstract: A statistical multistream description of quantum plasmas is formulated, using the Wigner-Poisson system as dynamical equations. A linear stability analysis of this system is carried out, and it is shown that a Landau-like damping of plane wave perturbations occurs due to the broadening of the background Wigner function that arises as a consequence of statistical variations of the wave function phase. The Landau-like damping is shown to suppress instabilities of the one- and two-stream type.
TL;DR: In this paper, the decoherence effects of 1/f noise in quantum two-level systems (TLSs) were investigated with a variety of power spectra, with linear or quadratic coupling relative to the eigenbasis of the unperturbed Hamiltonian.
Abstract: Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyze noise sources with a variety of power spectra, with linear or quadratic coupling, which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. To evaluate the dephasing time for transverse 1/f noise second-order contributions have to be taken into account. Manipulations of the quantum state of the TLS define characteristic time scales. We discuss the consequences for relaxation and dephasing processes.
TL;DR: In this article, the authors derived structural results about these quantum spaces, especially about their ideals and K-theory, from the general theory of graph algebras and showed that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle, respectively.
Abstract: The C
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-algebras of continuous functions on quantum spheres, quantum real projective spaces, and quantum complex projective spaces are realized as Cuntz-Krieger algebras corresponding to suitable directed graphs Structural results about these quantum spaces, especially about their ideals and K-theory, are then derived from the general theory of graph algebras It is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle, respectively
TL;DR: In this article, a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing is derived, and a projection measurement characterized by the irreducible representation theory of the special linear group SL is proposed.
Abstract: We derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing. We discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error probability goes to 0. As an asymptotically optimal measurement, we propose a projection measurement characterized by the irreducible representation theory of the special linear group SL(). Especially, in the spin-1/2 system, it is realized by the simultaneous measurement of the total momentum and a momentum of a specified direction. As a by-product, we obtain another proof of quantum Stein's lemma. In addition, an asymptotically optimal measurement is constructed in the quantum Gaussian case, and it is physically meaningful.
TL;DR: In this paper, the authors consider the form of the currentvoltage curves generated when tunneling spectroscopy is used to measure the energies of individual electronic energy levels in nanometer-scale systems.
Abstract: We consider the form of the current-voltage curves generated when tunneling spectroscopy is used to measure the energies of individual electronic energy levels in nanometer-scale systems. We point out that the voltage positions of the tunneling resonances can undergo temperature-dependent shifts, leading to errors in spectroscopic measurements that are proportional to the temperature. We do this by solving the set of rate equations that can be used to describe electron tunneling via discrete quantum states, for a number of cases important for comparison to experiments, including (1) when just one spin-degenerate level is accessible for transport, (2) when two spin-degenerate levels are accessible, with no variation in electron-electron interactions between eigenstates, and (3) when two spin-degenerate levels are accessible, but with variations in electron-electron interactions. We also comment on the general case with an arbitrary number of accessible levels. In each case we analyze the voltage positions, amplitudes, and widths of the current steps due to the quantum states.
16 Nov 2002
TL;DR: A definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems is proposed and the resulting complexity class is studied, which is denote QSZK/sub HV/.
Abstract: In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK/sub HV/. We prove several facts regarding this class, including: the following problem is a complete promise problem for QSZKHV: given instructions for preparing two mixed quantum states, are the states close together or far apart in the trace norm metric? This problem is a quantum generalization of the complete promise problem of Sahai and Vadhan (1997) for (classical) statistical zero-knowledge; QSZK/sub HV/ is closed under complement; QSZK/sub HV//spl sube/PSPACE. (At present it is not known if arbitrary quantum interactive proof systems can be simulated in PSPACE even for one-round proof systems); any polynomial-round honest verifier quantum statistical zero-knowledge proof system can be simulated by a two-message (i.e., one-round) honest verifier quantum statistical zero-knowledge proof system. Similarly, any polynomial-round honest verifier quantum statistical zero-knowledge proof system can be simulated by a three-message public-coin honest verifier quantum statistical zero-knowledge proof system. These facts establish close connections between classical statistical zero-knowledge and our definition for quantum statistical zero-knowledge, and give some insight regarding the effect of this zero-knowledge restriction on quantum interactive proof systems. The relationship between our definition and possible definitions of general (i.e., not necessarily honest) quantum statistical zero-knowledge are also discussed.
TL;DR: In this paper, the results of a continuous non-demolition atom number measurement are fed back to control the quantum state of the sample to produce deterministically reproducible spin squeezing.
Abstract: We propose a quantum feedback scheme for producing deterministically reproducible spin squeezing. The results of a continuous nondemolition atom number measurement are fed back to control the quantum state of the sample. For large samples and strong cavity coupling, the squeezing parameter minimum scales inversely with atom number, approaching the Heisenberg limit. Furthermore, ceasing the measurement and feedback when this minimum has been reached will leave the sample in the maximally squeezed spin state.