arXiv subjects

Charles H. Bennett

Publications and source records attributed to Charles H. Bennett.

26 records · Page 2Linked to original sources

arXiv1999

Entanglement-Assisted Classical Capacity of Noisy Quantum Channels

Prior entanglement between sender and receiver, which exactly doubles the classical capacity of a noiseless quantum channel, can increase the classical capacity of some noisy quantum channels by an arbitrarily large constant factor depending on the channel, relative to the best known classical capacity achievable without entanglement. The enhancement factor is greatest for very noisy channels, with positive classical capacity but zero quantum capacity. Although such quantum channels can be simulated classically, no violation of causality is implied, because the simulation requires at least as much forward classical communication as the entanglement-assisted classical capacity of the channel being simulated. We obtain exact expressions for the entanglement-assisted capacity of depolarizing and erasure channels in d dimensions.

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arXiv1998

Quantum Nonlocality without Entanglement

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles which also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.

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arXiv1997

Capacities of Quantum Erasure Channels

The quantum analog of the classical erasure channel provides a simple example of a channel whose asymptotic capacity for faithful transmission of intact quantum states, with and without the assistance of a two-way classical side channel, can be computed exactly. We derive the quantum and classical capacities for the quantum erasure channel and related channels, and compare them to the depolarizing channel, for which only upper and lower bounds on the capacities are known.

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arXiv1997

Strengths and Weaknesses of Quantum Computing

Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time, it is natural to ask whether all of NP can be efficiently solved in quantum polynomial time. In this paper, we address this question by proving that relative to an oracle chosen uniformly at random, with probability 1, the class NP cannot be solved on a quantum Turing machine in time $o(2^{n/2})$. We also show that relative to a permutation oracle chosen uniformly at random, with probability 1, the class $NP \cap coNP$ cannot be solved on a quantum Turing machine in time $o(2^{n/3})$. The former bound is tight since recent work of Grover shows how to accept the class NP relative to any oracle on a quantum computer in time $O(2^{n/2})$.

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arXiv1996

Entanglement-Enhanced Classical Communication on a Noisy Quantum Channel

We consider the problem of trying to send a single classical bit through a noisy quantum channel when two transmissions through the channel are available as a resource. Classically, two transmissions add nothing to the receiver's capability of inferring the bit. In the quantum world, however, one has the possible further advantage of entangling the two transmissions. We demonstrate that, for certain noisy channels, such entangled transmissions enhance the receiver's capability of a correct inference.

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arXiv1996

Mixed State Entanglement and Quantum Error Correction

Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbi- trary quantum state $|ξ\rangle$ can be transmitted at some rate Q through a noisy channel $χ$ without degradation. We prove that an EPP involving one- way classical communication and acting on mixed state $\hat{M}(χ)$ (obtained by sharing halves of EPR pairs through a channel $χ$) yields a QECC on $χ$ with rate $Q=D$, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts $D_1(M)$ and $D_2(M)$ that can be locally distilled from it by EPPs using one- and two-way classical communication respectively, and give an exact expression for $E(M)$ when $M$ is Bell-diagonal. While EPPs require classical communica- tion, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way com- munication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way com- munication is available. We exhibit a family of codes based on universal hash- ing able toachieve an asymptotic $Q$ (or $D$) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single- error-correcting quantum block code. We prove that {\em iff} a QECC results in high fidelity for the case of no error the QECC can be recast into a form where the encoder is the matrix inverse of the decoder.

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arXiv1995

Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.} singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transfrom one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{Ψ^-}$) distillable from mixed states $M$, showing $D(M)>0$ if $\bra{Ψ^-}M\ket{Ψ^-}>\half$.

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arXiv1995

Concentrating Partial Entanglement by Local Operations

If two separated observers are supplied with entanglement, in the form of $n$ pairs of particles in identical partly-entangled pure states, one member of each pair being given to each observer; they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally-entangled pairs of particles, for example Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves {\em entropy of entanglement}---the von Neumann entropy of the partial density matrix seen by either observer---with the yield of singlets approaching, for large $n$, the base-2 entropy of entanglement of the initial partly-entangled pure state. Conversely, any pure or mixed entangled state of two systems can be produced by two classically-communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.

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