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arXiv:quant-ph/0409109 · Physical Review Letters

Quantum Benchmark for Storage and Transmission of Coherent States

Klemens Hammerer, Michael M. Wolf, Eugene Simon Polzik, J. I. Cirac

Published Apr 22, 2005• 178 citations
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Abstract

We consider the storage and transmission of a Gaussian distributed set of coherent states of continuous variable systems. We prove a limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only. The obtained bound is tight and serves as a benchmark which has to be surpassed by quantum channels in order to outperform any classical strategy. The success in experimental demonstrations of quantum memories as well as quantum teleportation has to be judged on this footing.

DOI
10.1103/physrevlett.94.150503

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We consider the storage and transmission of a Gaussian distributed set of coherent states of continuous variable systems. We prove a limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only. The obtained bound is tight and serves as a benchmark which has to be surpassed by quantum channels in order to outperform any classical strategy. The success in experimental demonstrations of quantum memories as well as quantum teleportation has to be judged on this footing.
An experimental success criterion for continuous-variable quantum teleportation and memory is to surpass the limit of the average fidelity achieved by classical measure-and-prepare schemes with respect to a Gaussian-distributed set of coherent states. We present an alternative proof of the classical limit based on the familiar notions of state-channel duality and partial transposition. The present method enables us to produce a quantum-domain criterion associated with a given set of measured fidelities.
We present quantum fidelity benchmarks for continuous-variable (CV) quantum devices to outperform quantum channels which can transmit at most kkk-dimensional coherences for positive integers kkk. We determine an upper bound of an average fidelity over Gaussian distributed coherent states for quantum channels whose Schmidt class is kkk. This settles fundamental fidelity steps where the known classical limit and quantum limit correspond to the two end points of k=1k=1k=1 and $k=\ensuremath{\infty}$, respectively. It turns out that the average fidelity is useful to verify to what extent an experimental CV gate can transmit a high-dimensional coherence. The result is further extended to be applicable to general quantum operations or stochastic quantum channels. Although the fidelity is often associated with heterodyne measurements in quantum optics, we can also obtain similar criteria based on quadrature deviations determined via homodyne measurements.
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Teleportation and storage of continuous variable states of light and atoms are essential building blocks for the realization of large scale quantum networks. Rigorous validation of these implementations require identifying, and surpassing, benchmarks set by the most effective strategies attainable without the use of quantum resources. Such benchmarks have been established for special families of input states, like coherent states and particular subclasses of squeezed states. Here we solve the longstanding problem of defining quantum benchmarks for general pure Gaussian single-mode states with arbitrary phase, displacement, and squeezing, randomly sampled according to a realistic prior distribution. As a special case, we show that the fidelity benchmark for teleporting squeezed states with totally random phase and squeezing degree is 1/2, equal to the corresponding one for coherent states. We discuss the use of entangled resources to beat the benchmarks in experiments.