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arXiv:2107.04582 · Physical Review A

Coherence of quantum states after noiseless attenuation

S. U. Shringarpure, Cory M. Nunn, T. B. Pittman, J. D. Franson

Published Jan 6, 2022• 7 citations
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Abstract

Attenuating a quantum state using a beam splitter will introduce noise and decoherence. Here we show that heralding techniques can be used to attenuate Schr\"odinger cat states and squeezed vacuum states without any noise or decoherence [Mi\ifmmode \check{c}\else \v{c}\fi{}uda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Noiseless attenuation also preserves quantum interference effects in nonclassical states such as squeezed vacuum states.

DOI
10.1103/physreva.105.013704

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Attenuating a quantum state using a beam splitter will introduce noise and decoherence. Here we show that heralding techniques can be used to attenuate Schr"odinger cat states and squeezed vacuum states without any noise or decoherence [Mi\ifmmode \check{c}\else \v{c}\fi{}uda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Noiseless attenuation also preserves quantum interference effects in nonclassical states such as squeezed vacuum states.
Loss and decoherence are major problems in the transmission of nonclassical states of light over large distances. It was recently shown that the effects of decoherence can be reduced by applying a probabilistic noiseless attenuator before transmitting a quantum state through a lossy channel, followed by probabilistic noiseless amplification [M. Micuda, I. Straka, M. Mikova, M. Dusek, N. J. Cerf, J. Fiurasek, and M. Jezek, Phys. Rev. Lett. 109, 180503 (2012)]. Here we show that similar results can be obtained for certain kinds of macroscopic quantum states by squeezing the signal before transmission, followed by deterministic amplification and antisqueezing to restore the original amplitude of the state. This approach can greatly reduce the effects of decoherence in the transmission of non-Gaussian states, such as Schr\"odinger cat states, without any reduction in the data transmission rate.
The process of heralded noiseless amplification, and the inverse process of heralded noiseless attenuation, have potential applications in the context of quantum communications. Although several different physical implementations of heralded noiseless amplifiers have now been demonstrated, the research on heralded noiseless attenuators has been largely confined to a beam-splitter based approach. Here we show that an optical parametric amplifier (OPA), combined with appropriate heralding, can also serve as a heralded noiseless attenuator. The counterintuitive use of an optical amplifier as an attenuator is only possible due to the probabilistic nature of the device.
We show that superpositions of oppositely squeezed states -- non-Gaussian Schr{ö}dinger-cat-like states -- exhibit enhanced nonclassical features and provide an entanglement advantage in the small-squeezing regime. These states possess photon-number structures distinct from conventional coherent-state cat states, and we analyze their Wigner functions and the entanglement generated when they are injected into a 50-50 beam splitter. As a practical application, we demonstrate that they enable a high-quality heralded single-photon source whose second-order intensity correlation function is smaller than that obtained from a pure two-mode squeezed vacuum state. We further propose a linear-optical heralding scheme that approximates these superpositions without requiring strong Kerr nonlinearities. Our results indicate that the superposition of oppositely squeezed states is a promising non-Gaussian resource for quantum information processing, particularly for single-photon generation.
Recent work by Mi\ifmmode \check{c}\else \v{c}\fi{}uda et al. [Phys. Rev. Lett. 109, 180503 (2012)] suggests that pairing noiseless amplification with noiseless attenuation can conditionally suppress loss terms in the direct transmission of quantum states. Here we extend this work to entangled states: First, we explore bipartite states, specifically the two-mode squeezed vacuum and NOON states, and, second, we examine MMM-partite states, concentrating on W and Greenberger-Horne-Zeilinger (GHZ) states. In analogy with the original proposal, our results demonstrate that in each case under consideration, a correct combination of attenuation and amplification techniques before and after transmission through a pure loss channel can restore the initial quantum state. However, we find that for both W and NOON states, the noiseless attenuation is redundant and not required to achieve loss term suppression. This work clarifies the role of noiseless attenuation when paired with noiseless amplification for entanglement distribution and provides an operational example of how GHZ and W state entanglement differs.
Abstract We let a set of beam splitters of vacuum mode with a chosen transmittance parameter η in interaction with a separable coherent states. This model induces the production of an attenuated quantum channels based on entangled optical states. Indeed, the decoherence effect is exploited positively here to generate such kind of quantum channels. Next, the amplitude damping and the entanglement amount of these produced channels are enhanced thereafter by a probabilistic quasi amplification process using again a 50:50 beam splitter .