Showing papers on "Quantum channel published in 1995"

Quantum cryptography with coherent states

Abstract: The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a system, based on a symbiosis of two existing systems, for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation.

Quantum decoherence in mixed quantum‐classical systems: Nonadiabatic processes

Abstract: We address the issue of quantum decoherence in mixed quantum‐classical simulations. We demonstrate that restricting the classical paths to a single path among all the quantum paths affects a coarse graining of the quantum paths. Such coarse graining causes the quantum paths to lose coherence as the various possible classical paths associated with each quantum state diverge. This defines a reduction mapping of the quantum density matrix, and we derive a quantum master equation suitable for mixed quantum‐classical systems. The equation includes two terms: first, the ordinary quantum Liouvillian which is parametrized by a single classical path, and second, a quantum decoherence term that includes both a coherence time and length scale which are determined by the dynamics of the classical paths. Model calculations for electronic coherence loss in nonadiabatic mixed quantum‐classical dynamics are presented as examples. For a model charge transfer chemical reaction with nonadiabatic transitions, application of ...

Measurement of the bell operator and quantum teleportation

Abstract: We propose a scheme for measuring an optical version of the Bell operator, using a generalization of the Hong-Ou-Mandel interferometer. Discrete-mode calculations show this to be sufficient to allow teleportation of the state of polarization of a photon with a conditional efficiency approaching 100%. The feasibility of the scheme is investigated through full broadband calculations.

Dense Coding Based on Quantum Entanglement

Abstract: We analyse the Bennett-Wiesner dense quantum coding scheme for non-maximally entangled carriers of information. Our generalization shows that the detection scheme proposed by Bennett and Wiesner is optimal even when the entanglement is not perfect. We comment on the optical realization of the scheme.

Quantum Filtering of Markov Signals with White Quantum Noise

Abstract: Time-continuous non-anticipating processes of nondemolition measurements in quantum systems are described. In particular, the notion of physically realisable quantum filter is introduced and the problem of its optimisation to obtain the best a posteriori quantum state is considered. The fact that the optimal filtering of a quantum Markovian Gaussian signal with the Gaussian white quantum noise can be described by a coherent Markovian linear filter corresponding to quantum Gaussian state diffusion is proved. As an example, the problem of optimal measurement of complex amplitude for a quantum Markovian oscillator, loaded on a quantum wave communication line, is considered.

Mathematical techniques for quantum communication theory

Abstract: We present mathematical techniques for addressing two closely related questions in quantum communication theory. In particular, we give a statistically motivated derivation of the Bures-Uhlmann measure of distinguishability for density operators, and we present a simplified proof of the Holevo upper bound to the mutual information of quantum communication channels. Both derivations give rise to novel quantum measurements.

Macroscopic coherence via quantum feedback.

Abstract: It is shown that quantum-nondemolition-mediated feedback is able to preserve the interference fringes of the superposition of macroscopically distinguishable quantum states.

Projective quantum spaces

Abstract: Associated to the standard SUq(n) R-matrices, we introduce quantum spheresSq2n-1, projective quantum spaces ℂℙqn-1, and quantum Grassmann manifoldsGk(ℂqn). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzezinski and S. Majid.

On conjugate complex time and information in relativistic quantum theory

Abstract: The note presents some reflections on the mathematical utility of complex time in relativity and quantum theory. In particular we investigate duality particles in case of space-like and time-like characteristics when the rest mass is zero.

A quantum jump in computer science

Abstract: Classical and quantum information are very different. Together they can perform feats that neither could achieve alone. These include quantum computing, quantum cryptography and quantum teleportation. This paper surveys some of the most striking new applications of quantum mechanics to computer science. Some of these applications are still theoretical but others have been implemented.

Electron transport through one-dimensional lateral surface superlattices in magnetic fields

Abstract: A scattering-matrix method for the calculations of electron transport through lateral quantum systems in the presence of a perpendicular magnetic field is developed and is used to investigate the effects of an applied magnetic field on electron transport through a quantum channel modulated by a smooth periodic potential along the direction of the current flow. At zero magnetic field, the calculated conductance displays regular dips due to the formation of minigaps (or the Bragg reflections) and the rapid oscillations due to electron transmission through the coupled quasi-zero-dimensional states in the cavity regions between the potential barriers. Both are shown to be suppressed when a magnetic field is applied to the quantum channel. This is interpreted as the formation of propagating edge states. However, other irregular dips are shown to appear in the conductance of the modulated channel in the presence of the magnetic field. These dips reflect the coupling between the electron states propagating along the opposite edges of the channel and may appear so densely in a wide quantum channel with a strong modulation that the conductance exhibits fluctuations. In the high-field regime where the magnetic length ${\mathit{l}}_{\mathit{B}}$ is much smaller than the channel width w, these irregular dips are seen to be also suppressed, leading to a nearly perfect recovery of the conductance quantization.

Long-distance frequency-division interferometer for communication and quantum cryptography.

Abstract: We introduce and demonstrate experimentally a single-channel long-distance interferometer that utilizes frequency division of two optical waves by using acousto-optic devices at the transmitting and receiving nodes of the interferometer. This novel single-channel long-distance interferometer provides unity visibility of the interference and therefore is useful not only for remote sensing and optical communications but also for quantum cryptosystems applications.

Quantum Error Correction by Coding

Abstract: Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We propose a new technique based on the use of coding in order to detect and correct errors due to imperfect transmission lines in quantum cryptography or memories in quantum computers. We give a particular example of how to detect a decohered qubit in order to transmit or preserve with high fidelity the original qubit.

Quantum bound states in a double-bend quantum channel

Abstract: By use of the mode‐matching technique the quantum bound states in a double‐bend quantum channel of finite length connecting to two 2D electron gas reservoirs have been investigated in detail. The conductance G of the quantum system is calculated as a function of Fermi energy and the electron density associated with bound states. It is found that there exists one resonant peak in G corresponding to resonant tunneling via one quasibound state below the first conductance plateau for the quantum channel with double‐bend continuity and two resonant peaks in G corresponding to resonant tunneling via two quasibound states which are symmetric and antisymmetric superposition of two local bound states localized at two right‐angle bends below the first conductance plateau for the quantum channel with double‐bend discontinuity. At finite temperature the results are compared with experimental results and are found to explain them well.

Quantum Teleportation and Quantum Computation Based on Cavity QED

Abstract: Recently, Bennett et al. I have proposed a scheme for \"teleporting\" an unknown quantum state by splitting it up into a purely classical channel and a purely quantum channel. The quantum channel consists of a pair of particles with perfectly correlated spins, such as a spin singlet state of two spin-% particles (henceforth referred to as an EPR pair'). One of the two EPR particles is sent to the sender of the state (Alice) and the other is sent to the receiver (Bob). To send the unknown state (labeled lu)), which is also carried by a spin-5 particle, Alice makes a measurement in an entangled state basis (made up of the four orthogonal two-particle states of perfectly correlated spins) on the two-particle system consisting of the particle in the state lu ) and her EPR particle. She sends the result of her measurement (one of four possible outcomes) via a classical channel to Bob, who then applies one of four corresponding unitary transformations to his EPR particle, leaving it in the state lu). It is important to note that, in this scheme, Alice need not have any knowledge about the state lu), nor does she learn anything about l u ) in the teleportation process. The crucial point in the teleportation scheme is the measurement of the two-particle system in the basis of entangled states (also referred to as \"Bell states\"?). This type of measurement is also important for a related scheme, in which one can transmit two bits of information with a single two-level system, effectively doubling the channel ~apac i ty .~ In references 1 and 3, little discussion was devoted to how one could carry out the measurement of the two-particle system in the Bell-state basis. A Bell-state measurement of spin entangled particles using upconversion of a photon pair in a nonlinear crystal3 does not seem feasible due to its very low efficiency. On the other hand, a measurement by linear optical elements only cannot be performed unambigu~usly.~ In this report, we describe how one can use cavity QED techniques to produce EPR correlations and to make measurements in the Bell-state basis. This will form a basis for a specific implementation of the teleportation scheme of Bennett et u I . , ~ as well as that of encoding two bits of information on a single two-level system3 In these

Lower bound for mutual information of a quantum channel.

Abstract: We obtain a lower bound for the mutual information of a quantum transmission channel, which is perfectly analogous with Holevo's upper bound. The Uhlmann inequality for relative entropies is used, in a reverted order, for a completely positive mapping related with the mixed coherent states introduced by us seventeen years ago. Possible applications to quantum cryptography are discussed.

Spinor Representations of $U_q(\hat{\frak gl}(n))$ and Quantum Boson-Fermion Correspondence

Abstract: This is an extension of quantum spinor construction in \cite{DF2}. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak gl}(n))$ and explain classical and quantum boson-fermion correspondence.

Feedback in open quantum systems

Abstract: Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.

Quantum cryptography in noisy channels

Abstract: We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to EPR-based schemes. We also show that the performance of a noisy channel approaches that of a noiseless one as the error rate tends to zero. (i.e., the secrecy capacity $C_s (\epsilon) \to C_s (0)$ as $\epsilon \to 0$.) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard simply by assigning vastly different probabilities to the two conjugate bases.

Information Gain in Quantum Communication Channels

Abstract: In quantum communications the performances of an amplifier depend on the scheme of the channel in which the device is inserted. For example, both gain and noise figure of the amplifier depend on the kind of coding at the transmitter, and detection at the receiver. [1] In an optimized ideal channel, detection and coding are ideal, and both are “matched” on the same observable; the alphabet probability is optimized in order to satisfy the physical constraints on the line. In this case, the channel capacity is already achieved, and there is no need of amplification. However, when the channel is nonideal—either because of quantum mismatch between transmitter and receiver, because of losses along the line, or as a result of nonunit quantum efficiency at detectors—an appropriate amplification can improve the transmitted information, ideally achieving the channel capacity for infinite gain.

On an Effectiveness of Quantum Mini-Max Formula in Quantum Communication

Abstract: The quantum detection theory is much attractive in practical design problems of quantum communication systems because it can predict an ultimate performance of optical communication systems[1]. Recently many researchers have tried to apply the quantum Bayes formula to practical optical communication systems. In some case, unfortunately, the quantum Bayes formula can not provide analytical solutions because of the difficulties to solve the nonlinear equations for unknown variables. However, Hirota[2] showed the fact that the quantum mini-max formula may provide a simplification of the calculation process and this was confirmed for binary pure state signals, orthogonal signal for pure state, and others[3]. Especially, for ternary symmetric signal system, it is quite difficult to obtain an analytical solution in the case of Bayes. But the case of mini-max is solvable. Although the analytical solutions of the optimum detection operators are purely mathematical descriptions of the quantum detection process, they will provide the important information to the implementation problem designing a practical system with the minimum error probability, so-called “the optimum quantum receiver” [4,5].

A Mathematical Study of Information Transmission in Quantum Communication Processes

Abstract: In quantum communication theory, an input signal is represented by the quantum state. The input state changes under the influence of noise and loss associated with a channel. The attenuation process is a model of quantum channel describing an optical communication process. When an input state changes to an output state through a channel, the amount of information carried from the input state to the output state is represented by the quantum mutual entropy (information). The quantum communication theory has been studied by various researchers [4–7,11,13,15,16,18].

Type II quantum chaos

Abstract: A classification of quantum systems into three categories, type I, II and III, is proposed. The classification is based on the degree of sensitivity upon initial conditions, and the appearance of chaos. The quantum dynamics of type I systems is quasi periodic displaying no exponential sensitivity. They arise, e.g., as the quantized versions of classical chaotic systems. Type II systems are obtained when classical and quantum degrees of freedom are coupled. Such systems arise naturally in a dynamic extension of the first step of the Born-Oppenheimer approximation, and are of particular importance to molecular and solid state physics. Type II systems can show exponential sensitivity in the quantum subsystem. Type III systems are fully quantized systems which show exponential sensitivity in the quantum dynamics. No example of a type III system is currently established. This paper presents a detailed discussion of a type II quantum chaotic system which models a coupled electronic-vibronic system. It is argued that type II systems are of importance for any field systems (not necessarily quantum) that couple to classical degrees of freedom.

Quantum transport anomalies in semiconductor nanosystems

Abstract: We present quantum transport anomalies in the theoretical conductance of various semiconductor nanostructures. We first investigate a quantum channel with a chain of quantum boxes connected by slits, called a superlattice structure, and study the miniband and minigap effects associated with resonances and anti‐resonances in the conductance. We also report studies of electron transport in a quantum wire containing series or parallel slits and a detector slit. In these systems, strong conductance oscillations due to quantum interference effects are predicted as a detector slit is moved across the wire. In the case of a single and multi‐series slits, we attribute these effects to multiple reflections of the phase‐coherent electron along the quantum wire. The transmission coefficients and electronic phase shifts are examined, which provide insights into the origins of these conductance oscillations. In the case of multi‐parallel slits, peaks with two‐ (four‐) fold splitting in the conductance are exhibited du...

Bounds for Accessible Information in Quantum Mechanicsa

Abstract: Long before anyone else, John A. Wheeler saw a role for information theory in tackling the still-unresolved foundational questions of quantum mechanics. To pursue this grand vision, Wheeler exhorts us to begin building a structure of concrete technical results. We offer one such example here in honor of Wheeler's eighty-third birthday. A quantum communication channel is defined by the action of sending one of n possible messages, with prior probabi l i t i es~~, . . . ,p,, to a specified receiver in the form of one of n distinct (possibly mixed) density operators b l , . . . , f i n on an N-dimensional Hilbert space. The message states P I , together with their probabilities p,, constitute the message ensemble. At the end of the transmission, the receiver can perform any generalized quantum measurement described by a positive-operatorvalued measure (POVM) in an attempt to discern which message was actually sent. The fundamental question of quantum communication theory' is this: Which measurements maximize the Shannon mutual information about the actual message and just how much information is that maximal amount I,,,? Previous results on I,,, include an upper bound due to Holevo,\" a lower bound recently exhibited by Jozsa, Robb, and Wootters? and the classification of a few examples where I,,, can be calculated e x a ~ t l y . ~ ~ Of the two bounds, both are uniquely distinguished in the sense that they are the best bounds expressible solely in terms of the total density operator fi = Cp&, whenever all the fit are pure states. For this reason, however, both bounds are fairly loose for many message ensembles. Here, we derive ensemble-dependent bounds (an upper bound for the general channel and a lower bound for the binary channel) by way of reexamining and simplifying Holevo's original derivation. The quantum communication problem' is made precise through a formalization of the most general measurements allowed by quantum theory, the POVM.y A POVM is a set of nonnegative, Hermitian operators &, which are complete in the sense that z & , = 1 = (N-dimensional unit operator). The subscript b indexes the possible outcomes of the measurement; the conditions on the E b are just those necessary and sufficient for the quantity tr(bkh) to be a valid probability distribution.

Capacity of a memoryless quantum communication channel

Abstract: We introduce a proper framework of coding problems for a quantum memoryless channel and derive an asymptotic formula for the channel capacity having an operational significance. Some general lower and upper bounds for the quantum channel capacity are also derived.

Smart Card with Interferometric Quantum Cryptography Device

Abstract: We present an application of quantum cryptography with faint-pulse interferometry for smart-cards.