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arXiv:2409.03473

Purification of Gaussian States by Photon Subtraction

Kun Zhang, Hui‐jun Li, Jietai Jing, Nicolas Treps, Mattia Walschaers

Published Sep 5, 2024• 0 citations
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Abstract

Photon subtraction can enhance entanglement, which for pure states induces a decrease in the purity of reduced states. In contrast, by analyzing the purities of Gaussian states before and after subtracting a single photon, we prove that the purity of a Gaussian state can also be increased by less than 20%. On the one hand, it reveals that photon subtraction can reduce entanglement, and on the other hand, it reveals that it can achieve a limited amount of Gaussian state purification. Through the analysis of some examples, we demonstrate the inherent mechanism and applicable scope of photon-subtraction-based purification. In a multimode system, we find that photon subtraction can increase entanglement and purify some of the reduced states simultaneously. We thus present purification through the suppression of Gaussian noise as a new application for photon subtraction in continuous-variable quantum information processing.

DOI
10.48550/arxiv.2409.03473

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Photon subtraction can enhance entanglement, which for pure states induces a decrease in the purity of reduced states. In contrast, by analyzing the purities of Gaussian states before and after subtracting a single photon, we prove that the purity of a Gaussian state can also be increased by less than 20%. On the one hand, it reveals that photon subtraction can reduce entanglement, and on the other hand, it reveals that it can achieve a limited amount of Gaussian state purification. Through the analysis of some examples, we demonstrate the inherent mechanism and applicable scope of photon-subtraction-based purification. In a multimode system, we find that photon subtraction can increase entanglement and purify some of the reduced states simultaneously. We thus present purification through the suppression of Gaussian noise as a new application for photon subtraction in continuous-variable quantum information processing.
Photon subtraction (PS) can enhance entanglement, which, for pure states, induces a decrease in the purity of reduced states. In contrast, by analyzing the purities of Gaussian states before and after subtracting or adding a single photon, we prove that the purity of a Gaussian state can be increased by less than 20%. On the one hand, it reveals that PS and photon addition (PA) can reduce entanglement, and on the other hand, it shows that PS or PA can achieve a limited amount of Gaussian state purification. Through the analysis of several examples, we demonstrate the inherent mechanism and applicable scope of photon-subtraction-based purification. We further compare the performance between PS and PA for purifying single-mode Gaussian states, and analyze their capabilities in generating Wigner negativity within purification regimes. In a multimode system, we find that PS can simultaneously increase entanglement and purify some of the reduced states. These findings demonstrate the new application potential of PS and PA, specifically their capability to directly suppress Gaussian noise.
Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the Rényi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.
Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the R\'enyi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon.
Multimode photon subtraction provides an experimentally feasible option to construct large non-Gaussian quantum states in continuous variable quantum optics. The non-Gaussian features of the state can lead towards the more exotic aspects of quantum theory, such as negativity of the Wigner function. However, the payoff for states with such delicate quantum properties is their sensitivity to decoherence. In this paper, we present a general model that treats the most important source of decoherence in a purely optical setting: losses. We use the framework of open quantum systems and master equations to describe losses in nnn-photon-subtracted multimode states, where each photon can be subtracted in an arbitrary mode. As a main result, we find that mode-dependent losses and photon subtraction generally do not commute. In particular, the losses do not only reduce the purity of the state, they also change the modal structure of its non-Gaussian features. We then conduct a detailed study of single-photon subtraction from a multimode Gaussian state, which is a setting that lies within the reach of present-day experiments.
We investigate entanglement concentration of continuous-variable Gaussian states by local single-photon subtractions combined with local Gaussian operations. We first analyze the local squeezing-enhanced entanglement-concentration protocol proposed very recently by Zhang and van Loock [arXiv:1103.4500] and discuss the mechanism by which local squeezing before photon subtraction helps to increase the entanglement of the output state of the protocol. We next show that a similar entanglement improvement can be achieved by using local coherent displacements instead of single-mode squeezing.
The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.