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arXiv:quant-ph/0703158 · Physical Review Letters

Fidelity Criterion for Quantum-Domain Transmission and Storage of Coherent States Beyond the Unit-Gain Constraint

Ryo Namiki, Masato Koashi, Nobuyuki Imoto

Published Sep 4, 2008• 28 citations
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Abstract

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.

DOI
10.1103/physrevlett.101.100502

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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.
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.
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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.
The average fidelity of the teleportation of coherent states is calculated for general Gaussian bipartite systems shared by the partners of the protocol, Alice and Bob. It is considered that the shared Gaussian bipartite modes suffer independent attenuations before the processing of Alice and Bob. In addition, the classical communication between the partners can be controlled by a gain not necessarily unitary. Comparing with the classical fidelity threshold of measure-and-prepare methods, we establish several genuinely quantum teleportation conditions which depend on the gain and the local attenuations. If the gain can be tuned to maximize the bipartite state set capable of performing genuinely quantum teleportation, then a condition for teleportation robust against local attenuations is found. This condition is demonstrated to be essentially equivalent to the condition of robust Gaussian bipartite entanglement, obtained in previous articles, showing that the robustness against attenuations is an entanglement property relevant for characterization and application of bipartite systems. For the derivation of the robust teleportation conditions, the Gaussian operations onto the bipartite system are thoroughly studied, so that the transformations that maintain the fidelity invariant are found. Some scenarios for different Gaussian bipartite states are presented and discussed.