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Physical Review A

Optimal linear-optical noiseless quantum amplifiers driven by auxiliary multiphoton Fock states

Jaromı́r Fiurášek

Published Jun 15, 2022• 13 citations
Publisher

Abstract

Quantum scissors refer to interferometric schemes that allow combined teleportation and amplification of quantum states. Here, the author demonstrates that quantum scissors without feedforward can be optimized to have higher success probability than previously shown, and that quantum scissors can themselves be outperformed by generalized interferometric couplings.

DOI
10.1103/physreva.105.062425

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Quantum scissors refer to interferometric schemes that allow combined teleportation and amplification of quantum states. Here, the author demonstrates that quantum scissors without feedforward can be optimized to have higher success probability than previously shown, and that quantum scissors can themselves be outperformed by generalized interferometric couplings.
We generalize the concept of optical state truncation and noiseless linear amplification to enable truncation of the Fock-state expansion of an optical state to higher order and to simultaneously amplify it using linear optics. The resulting generalized quantum scissors are more efficient for noiseless linear amplification than employing multiple scissors in parallel and are experimentally practical. As a particular example, we focus on a third-order scissor device and demonstrate advantages in terms of fidelity with the target state, probability of success, distillable entanglement, and the amount of non-Gaussianity introduced.
A noiseless linear amplifier (NLA) can probabilistically amplify an optical state without the noise required by deterministic phase-insensitive amplification. We study a hybrid amplifier in which a finite-cutoff quantum-scissor NLA is placed between two single-mode squeezers. Analysis based on an ideal (infinite cutoff) NLA finds a gain enhancement from the squeezing. We explore the physics of this enhancement as the cutoff of the quantum scissors is increased. The low-cutoff sequence shows how this gain enhancement emerges from the truncated Fock space. Cutoff 3 is the lowest order at which the additional even- and odd-photon components can both contribute to gain enhancement, albeit with some skewing of the coefficients which reduces the fidelity. As the cutoff is increased the fidelity improves. However, unlike the ideal transformation, the finite-cutoff device depends on the phase of the coherent amplitude relative to the squeezing axes, with states aligned with the anti-squeezing requiring higher cutoffs to achieve high fidelity. We track behavior to high cutoffs and eventually see the performance predicted in the ideal theory emerge.
We examine heralded nondeterministic noiseless amplification based on the quantum scissors device, which has been shown to increase the one-photon amplitude of a state at the expense of the vacuum-state amplitude. Here we propose using the same basic design to perform perfect amplification in a basis set of up to two photons. The device is much more efficient than several one-photon amplifiers working in tandem. When used to amplify coherent states this advantage is shown either using fidelity or in terms of probability of successful action, or more strikingly in a combination of the two.
Nondeterministic quantum noiseless linear amplifiers are a new technology with interest in both fundamental understanding and new applications. With a noiseless linear amplifier it is possible to perform tasks such as improving the performance of quantum key distribution, purifying lossy channels, and distilling entanglement. Previous designs for noiseless linear amplifiers involving linear optics and photon counting are nonoptimal because they have a probability of success lower than the bound given by the theory of generalized quantum measurement. This paper develops a theoretical model using unitary interactions and projective measurements which reaches this limit. We calculate the fidelity and probability of success of this model for coherent states and Einstein-Podolsky-Rosen entangled states. Finally, we explore some examples of the complex interplay between the fidelity, probability, and the distilling and purifying power of the model.
A noiseless linear amplifier (NLA) performs the highest quality amplification allowable under the rules of quantum physics. Unfortunately, these same rules conspire against us via the no-cloning theorem, which constrains NLA operations to the domain of probabilistic processes. Nevertheless, they are useful for a wide variety of quantum protocols, with numerous proposals assuming access to an optimal NLA device which performs with the maximum possible success probability. Here we propose the first linear optics NLA protocol which asymptotically achieves this success probability bound, by modifying the Knill-Laflamme-Milburn near-deterministic teleporter into an amplifier.