Showing papers in "Physical Review A in 2003"
TL;DR: A protocol for quantum secure direct communication using blocks of Einstein-Podolsky-Rosen (EPR) pairs is proposed, and a set of ordered N EPR pairs is used as a data block for sending secret message directly.
Abstract: A protocol for quantum secure direct communication using blocks of Einstein-Podolsky-Rosen (EPR) pairs is proposed. A set of ordered N EPR pairs is used as a data block for sending secret message directly. The ordered N EPR set is divided into two particle sequences, a checking sequence and a message-coding sequence. After transmitting the checking sequence, the two parties of communication check eavesdropping by measuring a fraction of particles randomly chosen, with random choice of two sets of measuring bases. After insuring the security of the quantum channel, the sender Alice encodes the secret message directly on the message-coding sequence and sends them to Bob. By combining the checking and message-coding sequences together, Bob is able to read out the encoded messages directly. The scheme is secure because an eavesdropper cannot get both sequences simultaneously. We also discuss issues in a noisy channel.
1,580 citations
TL;DR: This work gives a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states, and proves its universality.
Abstract: We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation, and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of practical interest such as the circuit for quantum Fourier transformation and for the quantum adder. Finally, we describe computation with clusters of finite size.
1,370 citations
TL;DR: It will be shown that this algorithm performs an oracle search on a database of N items with $O(\sqrt{N})$ calls to the oracle, yielding a speedup similar to other quantum search algorithms.
Abstract: Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random-walk architecture that provides such a speedup. It will be shown that this algorithm performs an oracle search on a database of N items with $O(\sqrt{N})$ calls to the oracle, yielding a speedup similar to other quantum search algorithms. It appears that the quantum random-walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.
1,038 citations
TL;DR: In this article, the degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state, where the distance is defined as the distance from the point of view of the nearest neighbor.
Abstract: The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY. Acad. Sci. 755, 675 (1995); H. Barnum and N. Linden, J. Phys. A: Math. Gen. 34, 6787 (2001)], is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states. In particular, a detailed analysis is given for arbitrary mixtures of three-qubit Greenberger-Horne-Zeilinger, W, and inverted-W states. Along the way, we point out connections of the geometric measure of entanglement with entanglement witnesses and with the Hartree approximation method.
626 citations
TL;DR: In this paper, it was shown that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and small coherent superposition resource states.
Abstract: We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and "small" coherent superposition resource states.
623 citations
TL;DR: In this paper, the order rearrangement operation in both parties is controlled by a prior shared control key, which is used repeatedly in a quantum key distribution session, so that Eve cannot steal useful information.
Abstract: A technique is devised to perform orthogonal state quantum key distribution. In this scheme, entangled parts of a quantum information carrier are sent from Alice to Bob through two quantum channels. However, before the transmission, the order of the quantum information carrier in one channel is reordered so that Eve cannot steal useful information. At the receiver's end, the order of the quantum information carrier is restored. The order rearrangement operation in both parties is controlled by a prior shared control key which is used repeatedly in a quantum key distribution session.
452 citations
TL;DR: The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant \/2.
Abstract: The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck’s constant \/2 as demonstrated by Heisenberg’s thought experiment using a g-ray microscope Here it is shown that this common assumption is not universally true: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck’s constant when the intervention is dependent A model of measuring interaction with dependent intervention shows that Heisenberg’s lower bound for the noise-disturbance product is violated even by a nearly nondisturbing precise position measurement An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices
400 citations
TL;DR: In this article, a four-wave mixing (FWM) scheme in a five-level atomic system based on electromagnetically induced transparency (EIT) was analyzed.
Abstract: We analyze a four-wave-mixing (FWM) scheme in a five-level atomic system based on electromagnetically induced transparency (EIT). We show that EIT suppresses both two-photon and three-photon absorptions in the FWM scheme and enables the four-wave mixing to proceed through real, resonant intermediate states without absorption loss. The scheme results in a several orders of magnitude increase in the FWM efficiency in comparison with a recent scheme [Phys. Rev. Lett. 88, 143902 (2002)] and may be used for generating short-wavelength radiation at low pump intensities.
381 citations
TL;DR: In this article, the geometric structure of non-local gates is shown to be a 3-torus, and the invariants for local transformations are derived from the coordinates of the 3torus.
Abstract: We study nonlocal two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of nonlocal gates is a 3-torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-torus. Since different points on the 3-torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of nonlocal gates. We find that exactly half the nonlocal gates are perfect entanglers. We also investigate the nonlocal operations generated by a given Hamiltonian. We first study the gates that can be directly generated by a Hamiltonian. Then we explicitly construct a quantum circuit that contains at most three nonlocal gates generated by a two-body interaction Hamiltonian, together with at most four local gates generated by single-qubit terms. We prove that such a quantum circuit can simulate any arbitrary two-qubit gate exactly, and hence it provides an efficient implementation of universal quantum computation and simulation.
379 citations
TL;DR: In this paper, the authors derived necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multiparty multimode continuous-variable state.
Abstract: We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multiparty multimode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence, a complete state determination, for example, by detecting the entire correlation matrix of a Gaussian state, is not needed.
353 citations
TL;DR: Fault-tolerant quantum error correction networks are studied by a combination of numerical and approximate analytical treatments and it is found that concatenated codes based on the Golay code give higher thresholds than thoseBased on the $[[7,1,3]]$ Hamming code under most conditions.
Abstract: Fault-tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is calculated for a variety of Calderbank-Shor-Steane codes, including large block codes and concatenated codes. Recent insights into the syndrome extraction process, which render the whole process more efficient and more noise tolerant, are incorporated. The average number of recoveries that can be completed without failure is thus estimated as a function of various parameters. The main parameters are the gate $\ensuremath{\gamma}$ and memory $\ensuremath{\epsilon}$ failure rates, the physical scale-up of the computer size, and the time ${t}_{m}$ required for measurements and classical processing. The achievable computation size is given as a surface in parameter space. This indicates the noise threshold as well as other information. It is found that concatenated codes based on the $[[23,1,7]]$ Golay code give higher thresholds than those based on the $[[7,1,3]]$ Hamming code under most conditions. The threshold gate noise ${\ensuremath{\gamma}}_{0}$ is a function of $\ensuremath{\epsilon}/\ensuremath{\gamma}$ and ${t}_{m};$ example values are ${\ensuremath{\epsilon}/\ensuremath{\gamma}{,t}_{m},{\ensuremath{\gamma}}_{0}}={{1,1,10}^{\ensuremath{-}3}},$ ${0.01,1,3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}},$ ${{1,100,10}^{\ensuremath{-}4}},$ ${0.01,100,2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}},$ assuming zero cost for information transport. This represents an order of magnitude increase in tolerated memory noise, compared with previous calculations, which is made possible by recent insights into the fault-tolerant QEC process.
TL;DR: In this paper, it was shown that the limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations, and the violation of such local uncertainty relations may be used as an experimental test of entanglement generation.
Abstract: Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.
TL;DR: It is shown that $2n$ random classical bits are both necessary and sufficient for encrypting any unknown state of n quantum bits in an informationally secure manner and a connection is made between quantum encryption and quantum teleportation that allows for a different proof of optimality of teleportation.
Abstract: We show that $2n$ random classical bits are both necessary and sufficient for encrypting any unknown state of n quantum bits in an informationally secure manner. We also characterize the complete set of optimal protocols in terms of a set of unitary operations that comprise an orthonormal basis in a canonical inner product space. Moreover, a connection is made between quantum encryption and quantum teleportation that allows for a different proof of optimality of teleportation.
TL;DR: In this paper, the authors describe the use of time-multiplexing techniques that allow ordinary single-photon detectors, such as silicon avalanche photodiodes, to be used as photon-number-resolving detectors.
Abstract: Photon-number-resolving detectors are needed for a variety of applications including linear-optics quantum computing. Here we describe the use of time-multiplexing techniques that allow ordinary single-photon detectors, such as silicon avalanche photodiodes, to be used as photon-number-resolving detectors. The ability of such a detector to correctly measure the number of photons for an incident number state is analyzed. The predicted results for an incident coherent state are found to be in good agreement with the results of a proof-of-principle experimental demonstration.
TL;DR: In this paper, an extension of the well-known Bogoliubov theory to treat low-dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations is presented.
Abstract: We present an extension of the well-known Bogoliubov theory to treat low-dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretization in cells of size l. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two, and three dimensions with no ultraviolet or infrared divergence. Furthermore, this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, and the first order and second order correlation functions of the field. Explicit calculations are done for homogeneous systems.
TL;DR: In this article, the authors study the role of entanglement among subsystems in speeding up the dynamics of a composite system and establish the minimum time it takes for an initial state of mean energy E and energy spread E to move from its initial configuration by a predetermined amount.
Abstract: We establish the minimum time it takes for an initial state of mean energy E and energy spread $\ensuremath{\Delta}E$ to move from its initial configuration by a predetermined amount. Distances in Hilbert space are estimated by the fidelity between the initial and final states. In this context, we study the role of entanglement among subsystems in speeding up the dynamics of a composite system.
TL;DR: In this paper, it was shown that discord determines the difference between the efficiency of quantum and classical Maxwell's demons in extracting work from collections of correlated quantum systems, i.e., entities that can or cannot measure nonlocal observables or carry out conditional quantum operations.
Abstract: Quantum discord was proposed as an information-theoretic measure of the ``quantumness'' of correlations. I show that discord determines the difference between the efficiency of quantum and classical Maxwell's demons---that is, entities that can or cannot measure nonlocal observables or carry out conditional quantum operations---in extracting work from collections of correlated quantum systems.
TL;DR: In this article, the authors show that the form of the maximally entangled mixed states can vary with the combination of entanglement and mixedness measures chosen, and that for certain combinations, the forms can change discontinuously at a specific value of the entropy, along the way determining the states that, for a given value of entropy, achieve maximal violation of Bell's inequality.
Abstract: Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy. Along the way, we determine the states that, for a given value of entropy, achieve maximal violation of Bell's inequality.
TL;DR: In this paper, a variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation were used to analyze the dynamics of two-dimensional and three-dimensional condensates with a scattering length containing constant and harmonically varying parts.
Abstract: We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of two-dimensional (2D) and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation, without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.
TL;DR: In this article, a scheme for transferring quantum states from the propagating light fields to macroscopic, collective vibrational degree of freedom of a massive mirror by exploiting radiation pressure effects was proposed.
Abstract: We propose a scheme for transferring quantum states from the propagating light fields to macroscopic, collective vibrational degree of freedom of a massive mirror by exploiting radiation pressure effects. This scheme may prepare an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated movable mirrors by utilizing the entangled light fields produced from a nondegenerate optical parametric amplifier.
TL;DR: In this article, the experimental demonstration of quantum teleportation of the quadrature amplitudes of a light field was reported, and the experimental results were analyzed in terms of fidelity F and with signal transfer T-q =T++T- and noise correlation V-q=Vinparallel to out+Vin parallel to out.
Abstract: We report the experimental demonstration of quantum teleportation of the quadrature amplitudes of a light field. Our experiment was stably locked for long periods, and was analyzed in terms of fidelity F and with signal transfer T-q=T++T- and noise correlation V-q=Vinparallel to out+Vinparallel to out-. We observed an optimum fidelity of 0.64+/-0.02, T-q=1.06+/-0.02, and V-q=0.96+/-0.10. We discuss the significance of both T-q>1 and V-q<1 and their relation to the teleportation no-cloning limit.
TL;DR: In this paper, a magneto-optical trap was used to measure the Rb ns-np resonances for millimeter-wave transitions for 2-photon millimeter wave transitions, and the trap field was turned off and the 300-K atoms of the background Rb vapor were used to make useful measurements.
Abstract: By using a magneto-optical trap we have measured the Rb $ns\ensuremath{-}(n+1)s$ and ${\mathrm{nd}}_{j}{\ensuremath{-}(n+1)d}_{j}$ two-photon millimeter-wave transitions for $32l~nl~37,$ observing 100-kHz-wide resonances, in spite of the trap's 10 G/cm magnetic-field gradient, in which one might expect to observe resonances 5 MHz wide. This resolution is possible because of the similarity of the ${g}_{j}$ factors in the initial and final states. Under the same conditions, the single-photon ns-np resonances are \ensuremath{\sim}5 MHz wide. To make useful measurements of these intervals, we turned off the trap field and used the 300-K atoms of the background Rb vapor. Together these measurements improve the accuracy of the s, p, and d quantum defects by an order of magnitude.
TL;DR: In this paper, a duality between entangled states and separable states is derived from the duality of the hyperdeterminant and its singularities, and the single copy of pure entangled states is classified into an onion structure of every closed subset, similar to that by the local rank in the bipartite case.
Abstract: We find that multidimensional determinants ``hyperdeterminants,'' related to entanglement measures (the so-called concurrence, or 3-tangle for two or three qubits, respectively), are derived from a duality between entangled states and separable states. By means of the hyperdeterminant and its singularities, the single copy of multipartite pure entangled states is classified into an onion structure of every closed subset, similar to that by the local rank in the bipartite case. This reveals how inequivalent multipartite entangled classes are partially ordered under local actions. In particular, the generic entangled class of the maximal dimension, distinguished as the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the $ng~4$ qubits), contrary to the widely known bipartite or three-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical n-partite entangled states. Our classification is also useful for the mixed states.
TL;DR: In this article, a parametrization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed.
Abstract: A parametrization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parametrization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under local unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parametrization.
TL;DR: In this paper, a two-qubit Fourier transform using vibrational levels of the Raman-like transitions through the electronic state of a single molecule was investigated for up to five qubits, and the classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels.
Abstract: The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time-dependent Hamiltonian The inverse problem of finding the field that generates a specific unitary transformation is the subject of study The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space Optimal control theory is used to solve the inversion problem irrespective of the initial input state A unified formalism based on the Krotov method is developed leading to a different scheme The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ electronic state of ${\mathrm{Na}}_{2}$ Raman-like transitions through the $A{}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ electronic state induce the transitions Light fields are found that are able to implement the Fourier transform within a picosecond time scale Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse Of the schemes studied, the square modulus scheme converges fastest A study of the implementation of the Q qubit Fourier transform in the ${\mathrm{Na}}_{2}$ molecule was carried out for up to five qubits The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized
TL;DR: In this article, a general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations, which leads to the introduction of entanglement measures quantifying the multi-partite entenglement (as generalizations of the concurrence for two qubits and the 3-tangle for three qubits).
Abstract: A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence for two qubits and the 3-tangle for three qubits), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover, a natural extension of the definition of Greenberger-Horne-Zeilinger states to, e.g., 2x2xN systems is obtained.
TL;DR: In this paper, Coulomb exploded molecules with a high-intensity circularly polarized pulse and used an ion imaging detector to measure a series of two-dimensional projections of the wave packet's angular distribution in 27 fs increments.
Abstract: We use linearly polarized 45 fs pulses to create rotational wave packets in ${\mathrm{N}}_{2}$ and ${\mathrm{O}}_{2}.$ We Coulomb explode molecules with a high-intensity circularly polarized pulse and use an ion imaging detector to measure a series of two-dimensional projections of the wave packet's angular distribution in 27 fs increments. We highlight the evolving wave packet near the first, second, sixth, and tenth full revival times and also near the one-eighth, one-quarter, one-half, and three-quarter fractional revivals.
TL;DR: In this article, a scheme to achieve maximally entangled states, controlled phase shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity is presented.
Abstract: We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
TL;DR: In this article, a probabilistic controlled-not-gate for single photons was demonstrated using a single ancilla photon in a device constructed using linear optical elements, and the successful operation of the controlled-NOT gate relied on post-selected three-photon interference effects.
Abstract: We report a proof-of-principle demonstration of a probabilistic controlled-NOT gate for single photons. Single-photon control and target qubits were mixed with a single ancilla photon in a device constructed using only linear optical elements. The successful operation of the controlled-NOT gate relied on post-selected three-photon interference effects, which required the detection of the photons in the output modes.
TL;DR: In this paper, the photon-number-dependent parts in the effective Hamiltonian are canceled with the assistance of a strong classical field, which is insensitive to both the cavity decay and the thermal field.
Abstract: We propose a scheme for generating entangled states for two or more multilevel atoms in a thermal cavity. The photon-number-dependent parts in the effective Hamiltonian are canceled with the assistance of a strong classical field. Thus the scheme is insensitive to both the cavity decay and the thermal field. The scheme does not require individual addressing of the atoms in the cavity. The scheme can also be used to generate entangled states for many hot multilevel ions.