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arXiv:1404.2643 · Physical Review Letters

Quantum Benchmark via an Uncertainty Product of Canonical Variables

Ryo Namiki, Koji Azuma

Published Apr 6, 2015• 4 citations
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Abstract

We present an uncertainty-relation-type quantum benchmark for continuous-variable (CV) quantum channels that works with an input ensemble of Gaussian-distributed coherent states and homodyne measurements. It determines an optimal trade-off relation between canonical quadrature noises that is unbeatable by entanglement breaking channels and refines the notion of two quantum duties introduced in the original papers of CV quantum teleportation. This benchmark can verify the quantum-domain performance for all one-mode Gaussian channels. We also address the case of stochastic channels and the effect of asymmetric gains.

DOI
10.1103/physrevlett.114.140503

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We present an uncertainty-relation-type quantum benchmark for continuous-variable (CV) quantum channels that works with an input ensemble of Gaussian-distributed coherent states and homodyne measurements. It determines an optimal trade-off relation between canonical quadrature noises that is unbeatable by entanglement breaking channels and refines the notion of two quantum duties introduced in the original papers of CV quantum teleportation. This benchmark can verify the quantum-domain performance for all one-mode Gaussian channels. We also address the case of stochastic channels and the effect of asymmetric gains.
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.
Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian-distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.
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.
Continuous-variable (CV) quantum teleportation is usually benchmarked by average fidelity, but when the teleportation is repeatedly used within optical networks or measurement-based architectures, uniformity across the input ensemble becomes equally important. We analyze this issue using two complementary figures of merit: the average fidelity and the fidelity deviation, which quantifies the input dependence of the single-shot teleportation fidelity. We prove that any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. We then show that when a protocol raises the average fidelity through input-selective conditioning, the deviation generically increases in tandem, giving a quantitative universality cost. As a concrete example, we study teleportation enhanced by the so-called measurement-based noiseless linear amplification, where a heralded filter acts on the Bell-measurement record. The resulting trade-off among average fidelity, fidelity deviation, and success probability shows that stronger filtering can improve the conditional fidelity only by concentrating the successful events in favored regions of phase space, thereby suppressing the success probability and reducing input uniformity. Our results provide an operational framework for distinguishing genuine channel improvement from selectivity-driven post-selected advantage and suggest that the probabilistic CV teleportation should be assessed with average quality, universality, and heralding rate treated on an equal footing.
Given a certain amount of entanglement available as a resource, what is the most efficient way to accomplish a quantum task? We address this question in the relevant case of continuous variable quantum teleportation protocols implemented using two-mode Gaussian states with a limited degree of entanglement and energy. We first characterize the class of single-mode phase-insensitive Gaussian channels that can be simulated via a Braunstein-Kimble protocol with nonunit gain and minimum shared entanglement, showing that infinite energy is not necessary apart from the special case of the quantum limited attenuator. We also find that apart from the identity, all phase-insensitive Gaussian channels can be simulated through a two-mode squeezed state with finite energy, albeit with a larger entanglement. We then consider the problem of teleporting single-mode coherent states with Gaussian-distributed displacement in phase space. Performing a geometrical optimization over phase-insensitive Gaussian channels, we determine the maximum average teleportation fidelity achievable with any finite entanglement and for any realistically finite variance of the input distribution.