Showing papers by "Howard Barnum published in 2000"
TL;DR: It is shown that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel, and that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity.
Abstract: For the discrete memoryless quantum channel, we show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion for success in transmission, and that which uses the minimum fidelity of pure states in a subspace of the input Hilbert space as its criterion. As a corollary, any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity. We also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel. This enables us to simplify a known upper bound for the channel capacity. It also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity.
251 citations
TL;DR: In this paper, the authors show that Deutsch's derivation fails because it includes hidden probabilistic assumptions, such as the non-probabilistic part of classical decision theory.
Abstract: In a recent paper, Deutsch [1] claims to derive the “probabilistic predictions of quantum theory” from the “non-probabilistic axioms of quantum theory” and the “non-probabilistic part of classical decision theory.” We show that his derivation fails because it includes hidden probabilistic assumptions.
114 citations
TL;DR: This paper gives the first quantum circuit for computing f( 0)OR f( 1) more reliably than is classically possible with a single evaluation of the function.
Abstract: We give the first quantum circuit for computing f( 0)OR f( 1)more reliably than is classically possible with a single evaluation of the function. OR therefore joins XOR (i.e. parity, f( 0)f( 1)) to give the full set of logical connectives (up to relabelling of inputs and outputs) for which there is quantum speedup.
43 citations
TL;DR: I introduce rate-distortion theory for the coding of quantum information and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to store or compress an entangled quantum source with a given maximum level of distortion per source emission.
Abstract: I introduce rate-distortion theory for the coding of quantum information, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to store or compress an entangled quantum source with a given maximum level of distortion per source emission.
35 citations
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TL;DR: In this paper, the authors consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system, and exhibit an approximate reversal operation, adapted to the initial density operator and the ''noise'' dynamics to be reversed.
Abstract: We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the initial density operator and the ``noise'' dynamics to be reversed. We show that its error in preserving either quantum or classical information is no more than twice that of the optimal reversal operation. Applications to quantum algorithms and information transmission are discussed.
12 citations
TL;DR: In this article, the authors consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states, and prove upper and lower bounds and describe a series of illustrative examples of compression.
Abstract: We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.
4 citations
TL;DR: In this article, the Schumacher limit is shown to be at least as large as the quantum information content of a source E of pure quantum states with von Neumann entropy S. The authors show that if E can be compressed with arbitrarily high fidelity into A qubits/signal plus any amount of auxiliary classical storage, then A must still be approximately the same size as S of E, but only by an amount not exceeding the classical information specifying the subspace for a signal from the source.
Abstract: Consider a source E of pure quantum states with von Neumann entropy S. By the quantum source coding theorem, arbitrarily long strings of signals may be encoded asymptotically into S qubits/signal (the Schumacher limit) in such a way that entire strings may be recovered with arbitrarily high fidelity. Suppose that classical storage is free while quantum storage is expensive and suppose that the states of E do not fall into two or more orthogonal subspaces. We show that if E can be compressed with arbitrarily high fidelity into A qubits/signal plus any amount of auxiliary classical storage then A must still be at least as large as the Schumacher limit S of E. Thus no part of the quantum information content of E can be faithfully replaced by classical information. If the states do fall into orthogonal subspaces then A may be less than S, but only by an amount not exceeding the amount of classical information specifying the subspace for a signal from the source.