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arXiv:1011.2014 · Physical Review A

Fundamental quantum limits on phase-insensitive linear amplification and phase conjugation in a practical framework

Ryo Namiki

Published Apr 19, 2011• 13 citations
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Abstract

We present experimentally testable quantum limitations on the phase-insensitive linear amplification and phase conjugation with respect to the transformation of a Gaussian-distributed set of coherent states following the footing to assess the success of continuous-variable quantum teleportation and quantum memory devices. The results enable us to compare the real device with the quantum-limited device via the feasible input of coherent states.

DOI
10.1103/physreva.83.040302

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We present experimentally testable quantum limitations on the phase-insensitive linear amplification and phase conjugation with respect to the transformation of a Gaussian-distributed set of coherent states following the footing to assess the success of continuous-variable quantum teleportation and quantum memory devices. The results enable us to compare the real device with the quantum-limited device via the feasible input of coherent states.
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.
Quantum teleportation constitutes a fundamental tool for various applications in quantum communication and computation. However, state-of-the-art continuous-variable quantum teleportation is restricted to moderate fidelities and short-distance configurations. This is due to unavoidable experimental imperfections resulting in thermal decoherence during the teleportation process. Here we present a heralded quantum teleporter able to overcome these limitations through noiseless linear amplification. As a result, we report a high fidelity of 92% for teleporting coherent states using a modest level of quantum entanglement. Our teleporter in principle allows nearly complete removal of loss induced onto the input states being transmitted through imperfect quantum channels. We further demonstrate the purification of a displaced thermal state, impossible via conventional deterministic amplification or teleportation approaches. The combination of high-fidelity coherent state teleportation alongside the purification of thermalized input states permits the transmission of quantum states over significantly long distances. These results are of both practical and fundamental significance; overcoming long-standing hurdles en route to highly-efficient continuous-variable quantum teleportation, while also shining new light on applying teleportation to purify quantum systems from thermal noise.
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.
We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of 0.58pm0.020.58 \\pm 0.020.58pm0.02 was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.
We propose and theoretically analyze a teleportation-based scheme for the high-fidelity noiseless quantum amplification of coherent states of light. In our approach, the probabilistic noiseless quantum amplification operation is encoded into a suitable auxiliary two-mode entangled state and then applied to the input coherent state via continuous-variable quantum teleportation. The scheme requires conditioning on the outcomes of homodyne measurements in the teleportation protocol. In contrast to high-fidelity noiseless quantum amplifiers based on combination of conditional single-photon addition and subtraction, the present scheme requires only photon subtraction in combination with auxiliary Gaussian squeezed vacuum states. We first provide a pure-state description of the protocol which allows us to to clearly explain its principles and functioning. Next we develop a more comprehensive model based on phase-space representation of quantum states, that accounts for various experimental imperfections such as excess noise in the auxiliary squeezed states or limited efficiency of the single-photon detectors that can only distinguish the presence or absence of photons. We present and analyze predictions of this phase-space model of the noiseless teleamplifier.