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AIP conference proceedings

Fidelity criterion for quantum-domain continuous variable channels

Ryo Namiki, Masato Koashi, N. Imoto, Alexander I. Lvovsky

Published Jan 1, 2009• 0 citations
Publisher

Abstract

We provide a general quantum benchmark for transmission/storage of coherent states in terms of the average fidelity. It leads to another benchmark described in terms of an average quadrature noise. While the fidelity criterion provides a sufficient condition for quantum domain of any continuous variable channel, for Gaussian channels, it is turn out to be necessary and sufficient.

DOI
10.1063/1.3131289

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We provide a general quantum benchmark for transmission/storage of coherent states in terms of the average fidelity. It leads to another benchmark described in terms of an average quadrature noise. While the fidelity criterion provides a sufficient condition for quantum domain of any continuous variable channel, for Gaussian channels, it is turn out to be necessary and sufficient.
We generalize the experimental success criterion for quantum teleportation (memory) in continuous-variable quantum systems to be suitable for a non-unit-gain condition by considering attenuation (amplification) of the coherent-state amplitude. The new criterion can be used for a nonideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in the quantum domain.
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.
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 introduce witnesses for the average channel fidelity between a known target gate and an arbitrary unknown channel, for continuous-variable (CV) systems. These are observables whose expectation value yields a tight lower bound to the average channel fidelity in question, thus constituting a practical tool for benchmarking experimental CV gates. Our framework applies to a broad class of target gates. Here, we focus on three specific types of targets: multi-mode Gaussian unitary channels, single-mode coherent state amplifiers, and the single-mode (non-Gaussian) cubic phase gate, which is a crucial ingredient for CV universal quantum computation. Our witnesses are experimentally-friendly as they rely exclusively on Gaussian measurements, even for the non-Gaussian-target case. Moreover, in all three cases, they can be measured efficiently in the estimation error ϵ\epsilonϵ and failure probability Δ\DeltaΔ, as well as in the number of modes mmm for the Gaussian-target case. To end up with, our approach for the Gaussian-target case relies on an improved measurement scheme for Gaussian state-fidelity witnesses, which is polynomially and exponentially more efficient in mmm and Δ\DeltaΔ, respectively, than previous schemes. The latter constitutes an interesting byproduct result on its own. Our findings are relevant to the experimental validation of many-body quantum technologies.
Abstract We aim to devise feasible, efficient verification schemes for bosonic channels. To this end, we construct an average-fidelity witness that yields a tight lower bound for average fidelity plus a general framework for verifying optimal quantum channels. For both multi-mode unitary Gaussian channels and single-mode amplification channels, we present experimentally feasible average-fidelity witnesses and reliable verification schemes, for which sample complexity scales polynomially with respect to all channel specification parameters. Our verification scheme provides an approach to benchmark the performance of bosonic channels on a set of Gaussian-distributed coherent states by employing only two-mode squeezed vacuum states and local homodyne detections. Our results demonstrate how to perform feasible tests of quantum components designed for continuous-variable quantum information processing.