Showing papers on "Amplitude damping channel published in 1998"
TL;DR: This work presents a scheme of a quantum repeater that connects a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity.
Abstract: In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. Our scheme tolerates general errors on the percent level, it works with a polynomial overhead in time and a logarithmic overhead in the number of particles that need to be controlled locally.
2,787 citations
TL;DR: In this paper, a protocol for teleportation of a single mode of the electromagnetic field with high fidelity using squeezed-state entanglement and current experimental capability is presented, including the roles of finite quantum correlation and nonideal detection efficiency.
Abstract: Quantum teleportation is analyzed for states of dynamical variables with continuous spectra, in contrast to previous work with discrete (spin) variables. The entanglement fidelity of the scheme is computed, including the roles of finite quantum correlation and nonideal detection efficiency. A protocol is presented for teleporting the wave function of a single mode of the electromagnetic field with high fidelity using squeezed-state entanglement and current experimental capability.
1,351 citations
TL;DR: In this article, the capacity of a classical-quantum channel with arbitrary (possibly mixed) states was shown to be the maximum of the entropy bound with respect to all a priori distributions.
Abstract: It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland, and Wootters (1996), who proved the equality for the pure state channel.
1,032 citations
01 Jan 1998
TL;DR: It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions.
Abstract: It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland and Wooters, who proved the equality for the pure state channel.
810 citations
TL;DR: The best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input is established and an upper bound on the quantum capacity of the depolarizing quantum channel is derived.
Abstract: We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel.
468 citations
TL;DR: It is shown that different applications may result in different channel capacities, and upper bounds on several of these capacities are proved based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory.
Abstract: Noisy quantum channels may be used in many information-carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two nonclassical features of the coherent information are demonstrated: the failure of subadditivity, and the failure of the pipelining inequality. Both properties arise as a consequence of quantum entanglement, and give quantum information new features not found in classical information theory. The problem of a noisy quantum channel with a classical observer measuring the environment is introduced, and bounds on the corresponding channel capacity proved. These bounds are always greater than for the unobserved channel. We conclude with a summary of open problems.
409 citations
Book•
04 Mar 1998
TL;DR: Theory of Coherent Transport as mentioned in this paper, single-electron tunneling, and dissipative quantum systems are discussed in detail in Section 2.2.1.3.
Abstract: Theory of Coherent Transport. Quantization of Transport. Single-Electron Tunneling. Dissipative Quantum Systems. Driven Quantum Systems. Chaos, Coherence, and Dissipation. Indexes.
372 citations
TL;DR: In this article, a classical analogy of quantum mechanical entanglement using classical light beams is presented, which can be used to guide the intuition and a tool for visualizing abstract concepts in low-dimensional Hilbert spaces.
Abstract: A classical analogy of quantum mechanical entanglement is presented, using classical light beams. The analogy can be pushed a long way, only to reach its limits when we try to represent multiparticle, or nonlocal, entanglement. This demonstrates that the latter is of exclusive quantum nature. On the other hand, the entanglement of different degrees of freedom of the same particle might be considered classical. The classical analog cannot replace Einstein-Podolsky-Rosen type experiments, nor can it be used to build a quantum computer. Nevertheless, it does provide a reliable guide to the intuition and a tool for visualizing abstract concepts in low-dimensional Hilbert spaces.
287 citations
TL;DR: This paper aims to clarify the role of classical signal on quantum background noise in the development of quantum coding theorem and investigates the case of arbitrary states with bounded entropy.
Abstract: ContentsI. IntroductionII. General considerations § 1. Quantum communication channel § 2. Entropy bound and channel capacity § 3. Formulation of the quantum coding theorem. Weak conversionIII. Proof of the direct statement of the coding theorem § 1. Channels with pure signal states § 2. Reliability function § 3. Quantum binary channel § 4. Case of arbitrary states with bounded entropyIV. c-q channels with input constraints § 1. Coding theorem § 2. Gauss channel with one degree of freedom § 3. Classical signal on quantum background noise Bibliography
254 citations
TL;DR: A scheme based on quantum interference is proposed that iteratively improves the fidelity of distant entangled particles.
Abstract: A general photonic channel for quantum communication is defined. By means of local quantum computing with a few auxiliary atoms, this channel can be reduced to one with effectively less noise. A scheme based on quantum interference is proposed that iteratively improves the fidelity of distant entangled particles.
180 citations
TL;DR: In this paper, the authors proposed to measure the quantum state by coupling a single-electron transistor to the $q$-bit and analyzed the time evolution of the density matrix of the transistor and the quantum bit when a voltage is turned on.
Abstract: Low-capacitance Josephson junction systems as well as coupled quantum dots, in a parameter range where single charges can be controlled, provide physical realizations of quantum bits, discussed in connection with quantum computing. The necessary manipulation of the quantum states can be controlled by applied gate voltages. In addition, the state of the system has to be read out. Here we suggest to measure the quantum state by coupling a single-electron transistor to the $q$-bit. As long as no transport voltage is applied, the transistor influences the quantum dynamics of the $q$-bit only weakly. We have analyzed the time evolution of the density matrix of the transistor and $q$-bit when a voltage is turned on. For values of the capacitances and temperatures which can be realized by modern nanotechniques, the process constitutes a quantum measurement process.
TL;DR: In this article, a quantum information theory that allows for a consistent description of entanglement is presented. But it is based entirely on density matrices rather than probability distributions for the description of quantum ensembles.
TL;DR: This was significantly extended from the previous article quant-ph/9705043,especially in an information theoretic aspect, by adding new results.
Abstract: We consider a channel coding for sending classical information through a quantum channel with a given ensemble of quantum states (letter states). As is well known, it is generically possible in a quantum channel that the transmittable information in block coding of length $n$ can exceed $n$ times the maximum amount that can be sent without any coding scheme. This so-called superadditivity in classical capacity of a quantum channel is a distinct feature that cannot be found in a classical memoryless channel. In this paper, a practical model of channel coding that shows this property is presented. It consists of a simple code-word selection and the optimum decoding of the code words minimizing the average error probability. At first, optimization of decoding strategy is discussed. Then the channel coding that shows the superadditivity in classical capacity is demonstrated.
TL;DR: In this paper, the authors derive a simple relation between a quantum channel's capacity to convey coherent (quantum) information and its usefulness for quantum cryptography, and derive the relation between quantum channel capacity and quantum cryptography.
Abstract: We derive a simple relation between a quantum channel's capacity to convey coherent (quantum) information and its usefulness for quantum cryptography.
TL;DR: In this article, the thermodynamic cost of error correction is analyzed and it is shown that error correction can be regarded as a kind of 'Maxwell demon', for which there is an entropy cost associated with information obtained from measurements performed during error correction.
Abstract: Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error–correcting codes, teleportation and reversing quantum measurements. We derive information–theoretic conditions and equivalent algebraic conditions that are necessary and sufficient for a general quantum operation to be reversible. We analyse the thermodynamic cost of error correction and show that error correction can be regarded as a kind of `Maxwell demon', for which there is an entropy cost associated with information obtained from measurements performed during error correction. A prescription for thermodynamically efficient error correction is given.
TL;DR: In this paper, the authors investigated dissipative quantum transport in extended periodic systems that are subjected to electric harmonic mixing fields and found that the quantum current exhibits multiple reversals when driven in the nonadiabatic regime.
Abstract: We investigate dissipative quantum transport in extended periodic systems that are subjected to electric harmonic mixing fields Ehm(t) = E1cos (Ωt) + E2cos (2Ωt + ). Although such a drive possesses no net bias on average, the interplay of quantum dissipation and nonlinear response causes a finite directed current. We thus discover the paradigm of a dissipative quantum rectifier. The quantum current exhibits multiple reversals when driven in the nonadiabatic regime. As a function of temperature the quantum current displays a bell-shaped characteristic–constituting the benchmark for quantum stochastic resonance. Moreover, harmonic mixing also serves as a novel tool to selectively control quantum diffusion.
TL;DR: Some basic properties of coding theory of a general quantum communication channel and its operational capacity are explored, including adaptive measurement with feedback code, reconsideration of single-letterized capacity formula, and pseudoclassicality of a channel.
Abstract: We explore some basic properties of coding theory of a general quantum communication channel and its operational capacity, including: 1) adaptive measurement with feedback code; 2) reconsideration of single-letterized capacity formula; and 3) pseudoclassicality of a channel.
TL;DR: In this paper, the real-time dynamics of quantum models with long-range interactions coupled to a heat-bath within the closed-time pathintegral formalism were studied and it was shown that quantum fluctuations depressed the transition temperature.
Abstract: We study the real-time dynamics of quantum models with long-range interactions coupled to a heat-bath within the closed-time path-integral formalism. We show that quantum fluctuations depress the transition temperature. In the subcritical region there are two asymptotic time-regimes with (i) stationary, and (ii) slow aging dynamics. We extend the quantum fluctuation-dissipation theorem to the nonequilibrium case in a consistent way with the notion of an effective temperature that drives the system in the aging regime. The classical results are recovered for $\hbar\to 0$.
TL;DR: In this article, an error prevention procedure based on two-particle encoding is proposed for protecting an arbitrary unknown quantum state from dissipation, such as phase damping and amplitude damping.
Abstract: An error prevention procedure based on two-particle encoding is proposed for protecting an arbitrary unknown quantum state from dissipation, such as phase damping and amplitude damping. The schemes, which exhibits manifestation of the quantum Zeno effect, is effective whether quantum bits are decohered independently or cooperatively. We derive the working condition of the scheme, and argue that this procedure has feasible practical implementation.
TL;DR: In this article, a class of optimal quantum codes for preventing collective amplitude damping to a reservoir at zero temperature was presented, where two quantum bits (qubits) are enough to protect one bit quantum information, and approximately $L+ √ 1/2 √ log(L/2 ) qubits are sufficient to protect L-qubit information when L is large.
Abstract: Collective decoherence is possible if the distance between quantum bits is smaller than the effective wavelength of the noise field. Collectivity in the decoherence helps us to devise more efficient quantum codes. We present a class of optimal quantum codes for preventing collective amplitude damping to a reservoir at zero temperature. It is shown that two quantum bits (qubits) are enough to protect one bit quantum information, and approximately $L+\frac{1}{2}{\mathrm{ln}}_{2}(\ensuremath{\pi}L/2)$ qubits are enough to protect L-qubit information when L is large. For preventing collective amplitude damping, these codes are much more efficient than the previously discovered quantum error correcting or avoiding codes.
17 Feb 1998
TL;DR: In this article, a new quantification of entanglement of a general (mixed) quantum state for a bipartite system was introduced, which is called Entanglement Of Assistance (EoA).
Abstract: The newfound importance of "entanglement as a resource" in quantum computation and quantum communication behooves us to quantify it in as many distinct ways as possible. Here we explore a new quantification of entanglement of a general (mixed) quantum state for a bipartite system, which we name entanglement of assistance. We show it to be the maximum of the average entanglement over all ensembles consistent with the density matrix describing the bipartite state. With the help of lower and upper bounds we calculate entanglement of assistance for a few cases and use these results to show the surprising property of superadditivity. We believe that this may throw some light on the question of additivity of entanglement of formation.
TL;DR: In this article, it was shown that phase discontinuity is an intrinsic property of single electron transport and arises from interference between two different transmission channels belonging to a localized state in the dot and a continuous state of the quantum channel.
Abstract: In a recent phase experiment by Schuster et al. [Nature 385, 417 (1997)], an abrupt phase drop of \ensuremath{\pi} was observed when the electron transmission through a quantum dot embedded in a quantum channel vanished. We show, both analytically and numerically, that this phase discontinuity is an intrinsic property of single electron transport: It arises from interference, known as Fano resonance, between two different transmission channels belonging to a localized state in the dot and a continuous state of the quantum channel. This phase behavior should also be seen in the same type of scattering resonances in other physical systems.
Posted Content•
TL;DR: This work presents a scheme of a quantum repeater that connects a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity.
Abstract: In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. The scheme tolerates general errors on the percent level.
TL;DR: This work investigates quantum Brownian motion sustained transport in both, adiabatically rocked ratchet systems and quantum stochastic resonance (QSR), finding that nonadiabatic driving may cause driving-induced coherences and quantized resonant transitions with no classical analog.
Abstract: We investigate quantum Brownian motion sustained transport in both, adiabatically rocked ratchet systems and quantum stochastic resonance (QSR). Above a characteristic crossover temperature T0 tunneling events are rare; yet they can considerably enhance the quantum-noise-driven particle current and the amplification of signal output in comparison to their classical counterparts. Below T0 tunneling prevails, thus yielding characteristic novel quantum transport phenomena. For example, upon approaching T=0 the quantum current in Brownian motors exhibits a tunneling-induced reversal, and tends to a finite limit, while the classical result approaches zero without such a change of sign. As a consequence, similar current inversions generated by quantum effects follow upon variation of the particle mass or of its friction coefficient. Likewise, in this latter regime of very low temperatures the tunneling dynamics becomes increasingly coherent, thus suppressing the semiclassically predicted QSR. Moreover, nonadiab...
16 Aug 1998
TL;DR: In the Arimoto-Blahut algorithm for computing the capacity of a classical discrete memoryless channel, maximization of the mutual information is converted to more tractable alternating maximizations of a two-variable function.
Abstract: In the Arimoto-Blahut (1972) algorithm for computing the capacity of a classical discrete memoryless channel, maximization of the mutual information is converted to more tractable alternating maximization of a two-variable function. We apply the same idea to computation of the capacity of a quantum memoryless channel.
TL;DR: It is shown that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information, and the coherent information maximized over all sources and block sizes, but not encodings, is used to bound the quantum capacity.
Abstract: We show that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information. This allows us to use the coherent information maximized over all sources and block sizes, but not encodings, to bound the quantum capacity. We perform an explicit calculation of this maximum coherent information for the quantum erasure channel and apply the bound in order find the erasure channel's capacity without relying on an unproven assumption as in an earlier paper.
TL;DR: In this paper, it was shown that the information provided by a specified distributed apparatus of n units in the measurement of a quantum state is bounded by 3.7 x n^(1/2) bits.
Abstract: We investigate the information provided about a specified distributed apparatus of n units in the measurement of a quantum state. It is shown that, in contrast to such measurement of a classical state, which is bounded by log (n+1) bits, the information in a quantum measurement is bounded by 3.7 x n^(1/2) bits. This means that the use of quantum apparatus offers an exponential advantage over classical apparatus.
TL;DR: Several upper bounds on the rate at which quantum information can be transmitted reliably via a noisy channel are examined, with an asymptotically vanishing average loss while the one-symbol loss of the channel is nonzero.
Abstract: In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if the loss is zero, quantum information can be perfectly transmitted at a rate measured by the quantum source entropy. By using block coding based on sequences of n entangled symbols, the average loss (defined as the overall loss of the joint n-symbol channel divided by n, when n→∞) can be made lower than the loss for a single use of the channel. In this context, we examine several upper bounds on the rate at which quantum information can be transmitted reliably via a noisy channel, that is, with an asymptotically vanishing average loss while the one-symbol loss of the channel is nonzero. These bounds on the channel capacity rely on the entropic Singleton bound on quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we analyze the Singleton bounds when the noisy quantum channel is supplemented with a classical auxiliary channel.
TL;DR: In this paper, a new interpretation of entanglement entropy is proposed, which is an index of the efficiency of quantum teleportation, and the implications for information loss problem and Hawking radiation are discussed.
Abstract: A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of Hilbert space into two subspaces 1 and 2 is an amount of information which can be transmitted through 1 and 2 from a system interacting with 1 to another system interacting with 2. The transmission medium is the quantum entanglement between 1 and 2. In order to support the interpretation, suggestive arguments are given: variational principles in entanglement thermodynamics and quantum teleportation. It is shown that a quantum state having maximal entanglement entropy plays an important role in quantum teleportation. Hence the entanglement entropy is, in some sense, an index of the efficiency of quantum teleportation. Finally, the implications for the information loss problem and Hawking radiation are discussed.
TL;DR: A nonlinear channel for a quantum teleportation process is rigorously constructed and the quantum mutual entropy is applied to characterize the quantum teleportation processes of Bennett et al.