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Advanced Quantum Technologies

Generating Discorrelated States for Quantum Information Protocols by Coherent Multimode Photon Addition

Nicola Biagi, Luca S. Costanzo, Marco Bellini, Alessandro Zavatta

Published Apr 6, 2021• 6 citations
Publisher

Abstract

Abstract It is demonstrated that the recently developed technique of delocalized single photon addition may generate discorrelation, a new joint statistical property of multimode quantum light states, whereby the number of photons in each mode can take any value individually, but two modes together never exhibit the same. By coherently adding a single photon to two identical coherent states of light in different temporal modes, the first experimental observation of discorrelation is provided. The capability of manipulating this statistical property has applications in scenarios involving the secure distribution of information among untrusted parties, like in the so‐called “mental poker” games.

DOI
10.1002/qute.202000141

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Abstract It is demonstrated that the recently developed technique of delocalized single photon addition may generate discorrelation, a new joint statistical property of multimode quantum light states, whereby the number of photons in each mode can take any value individually, but two modes together never exhibit the same. By coherently adding a single photon to two identical coherent states of light in different temporal modes, the first experimental observation of discorrelation is provided. The capability of manipulating this statistical property has applications in scenarios involving the secure distribution of information among untrusted parties, like in the so‐called “mental poker” games.
The statistical properties of photons are fundamental to investigating quantum mechanical phenomena using light. In multiphoton, two-mode systems, correlations may exist between outcomes of measurements made on each mode which exhibit useful properties. Correlation in this sense can be thought of as increasing the probability of a particular outcome of a measurement on one subsystem given a measurement on a correlated subsystem. Here, we show a statistical property we call "discorrelation", in which the probability of a particular outcome of one subsystem is reduced to zero, given a measurement on a discorrelated subsystem. We show how such a state can be constructed using readily available building blocks of quantum optics, namely coherent states, single photons, beam splitters and projective measurement. We present a variety of discorrelated states, show that they are entangled, and study their sensitivity to loss.
We present a concise review of recent experimental results concerning the conditional implementation of coherent superpositions of single-photon additions onto distinct field modes. Such a basic operation is seen to give rise to a wealth of interesting and useful effects, from the generation of a tunable degree of entanglement to the birth of peculiar correlations in the photon numbers and the quadratures of multimode, multiphoton, states of light. The experimental investigation of these properties will have an impact both on fundamental studies concerning, for example, the quantumness and entanglement of macroscopic states, and for possible applications in the realm of quantum-enhanced technologies.
We studied the effect of delocalized single-photon addition (DPA ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}^{\ifmmode\dagger\else\textdagger\fi{}}+{e}^{i\ensuremath{\varphi}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{2}^{\ifmmode\dagger\else\textdagger\fi{}}$) on two input modes containing four cases: two independent coherent states (CSs), two independent thermal states (TSs), two independent single-mode squeezed vacuums (SVs), and an entangled two-mode squeezed vacuum (TMSV). In essence, four types of non-Gaussian entangled light states are generated. We studied three different resources (including entanglement, discorrelation, and Wigner negativity) for each two-mode light state. The output states after DPA are entangled, with more parameters and complex structures, characterizing more Wigner negativity or even discorrelation. In contrast, the CSs case is the most tunable protocol, because its negativity under partial transposition, discorrelation, and Wigner logarithmic negativity are more sensitive to superposition phase $\ensuremath{\varphi}$ than those in TSs, SVs, and TMSV cases.
The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this paper we derive the truncated correlations, which are multimode generalizations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum.
We develop a general theory to describe the manipulation of a multimode quantum state of light via the subtraction of a single photon. The theory is applicable for various types of subtraction schemes independent of the physical nature of the light modes, their number or the embedded quantum states. We show that different subtraction schemes can be described in a unified approach through the characterization of their intrinsic subtraction modes. The conditional state of the multimode quantum light after the photon subtraction is defined by the number of subtraction modes and their matching with the light modes. We propose the manipulation of light states by controlling the subtraction modes. Performing a photon subtraction on a multimode quantum resource is promising for the implementation of a number of quantum information protocols in all-optical, multiplexed and scalable way.