Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Information

INTERFERENCE OF MULTI-MODE GAUSSIAN STATES AND "NON APPEARANCE" OF QUANTUM CORRELATIONS

Stefano Olivares

Published Dec 1, 2012• 1 citation
Publisher

Abstract

We theoretically investigate bilinear, mode-mixing interactions involving two modes of uncorrelated multi-mode Gaussian states. In particular, we introduce the notion of "locally the same states" (LSS) and prove that two uncorrelated LSS modes are invariant under the mode mixing, i.e. the interaction does not lead to the birth of correlations between the outgoing modes. We also study the interference of orthogonally polarized Gaussian states by means of an interferometric scheme based on a beam splitter, rotators of polarization and polarization filters.

DOI
10.1142/s0219749912410043

Related papers

DYNAMICS OF QUANTUM CORRELATIONS OF TWO INTERFERING BIPARTITE GAUSSIAN STATES

Stefano Olivares

We address the interference of a pair of two-mode Gaussian states, interacting pairwise through a beam-splitter Hamiltonian. In the framework of a suitable phase-space analysis, the correlations generated through the interaction are studied by considering a quantity proportional to the variance of difference between the detected photocurrents of all the possible couples of modes. We use this quantity to demonstrate the invariance through the interaction and the correlations swapping also in the presence of nonideal photodetection.

International Journal of Quantum Information•Oct 1, 2011•0 citations

Revealing interference by continuous variable discordant states

Alice Meda, Stefano Olivares, Ivo Pietro Degiovanni +3 more

In general, a pair of uncorrelated Gaussian states mixed in a beam splitter (BS) produces a correlated state at the output. However, when the inputs are identical Gaussian states the output state is equal to the input, and no correlations appear, as the interference had not taken place. On the other hand, since physical phenomena do have observable effects, and the BS is there, a question arises on how to reveal the interference between the two beams. We prove theoretically and demonstrate experimentally that this is possible if at least one of the two beams is prepared in a discordant, i.e., Gaussian correlated, state with a third beam. We also apply the same technique to reveal the erasure of polarization information. Our experiment involves thermal states and the results show that Gaussian discordant states, even when they show a positive Glauber P-function, may be useful to achieve specific tasks.

Optics Letters•Aug 9, 2013•7 citations

Detecting Gaussian entanglement via local quantities

Shuangshuang Fu, Shunlong Luo, Yue Zhang

Entanglement detection and quantification usually require the knowledge of correlations and thus is a global issue. For both theoretical and practical reasons, it is desirable to characterize entanglement via local quantities. Of course, this can only be achieved in special setups with some underlying structure encoding the correlations. For the often encountered bilinear interactions such as beamsplitter experiments, we propose an operational and friendly entanglement criterion for the two-mode Gaussian output states. Specifically, we show that in order to detect and evaluate the entanglement of the output states of a bilinear interaction involving uncorrelated Gaussian input states, we do not need to know the joint covariance matrix of the whole two-mode output states. Instead, we only need the respective covariances of the reduced states of the two input modes and that of the two output modes, which are all local quantities pertaining to a single mode and can be easily measured locally without explicitly considering the correlations between the modes. This is achieved by exploiting the input-output characteristics of bilinear interactions. The result recasts the celebrated entanglement criteria of Simon ( Phys. Rev. Lett. , 84 (2000) 2726) and Duan et al . ( Phys. Rev. Lett. , 84 (2000) 2722) into a more convenient and simple form.

Europhysics Letters (EPL)•Jul 1, 2021•2 citations

Unitarily localizable entanglement of Gaussian states

Alessio Serafini, Gerardo Adesso, Fabrizio Illuminati

We consider generic $(m\ifmmode\times\else\texttimes\fi{}n)$-mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as $(m+n)$-mode Gaussian states invariant under local mode permutations on the $m$-mode and $n$-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of $m+n\ensuremath{-}2$ uncorrelated single-mode states. The entanglement between the $m$-mode and the $n$-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of $(m+n)$-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes.

arXiv:quant-ph/0411109•Physical Review A•Mar 30, 2005•132 citations

Entanglement in quantum-optical bilinear devices

Matteo G. A. Paris

We examine the entanglement arising from the bilinear coupling of two nearly single-mode optical beams. We consider both the case of active and passive linear devices. The two modes are initially prepared in a pair of uncorrelated pure Gaussian states, and the degree of entanglement is analytically evaluated in terms of the excess information entropy at the output. A general formula is obtained and relevant cases are analysed in some detail.

Journal of Optics B Quantum and Semiclassical Optics•Jan 1, 1999•4 citations

Interplay of nonclassicality and entanglement of two-mode Gaussian fields generated in optical parametric processes

Ievgen I. Arkhipov, Jan Peřina, Jan Peřina +1 more

The behavior of general nonclassical two-mode Gaussian states at a beam splitter is investigated. Single-mode nonclassicality as well as two-mode entanglement of both input and output states are analyzed suggesting their suitable quantifiers. These quantifiers are derived from local and global invariants of linear unitary two-mode transformations such that the sum of input (or output) local nonclassicality measures and entanglement measure gives a global invariant. This invariant quantifies the global nonclassicality resource. Mutual transformations of local nonclassicalities and entanglement induced by the beam splitter are analyzed considering incident noisy twin beams, single-mode noisy squeezed vacuum states, and states encompassing both squeezed states and twin beams. A rich tapestry of interesting nonclassical output states is predicted.

arXiv:1605.07375•Physical Review A•Jul 5, 2016•29 citations
We theoretically investigate bilinear, mode-mixing interactions involving two modes of uncorrelated multi-mode Gaussian states. In particular, we introduce the notion of "locally the same states" (LSS) and prove that two uncorrelated LSS modes are invariant under the mode mixing, i.e. the interaction does not lead to the birth of correlations between the outgoing modes. We also study the interference of orthogonally polarized Gaussian states by means of an interferometric scheme based on a beam splitter, rotators of polarization and polarization filters.
We address the interference of a pair of two-mode Gaussian states, interacting pairwise through a beam-splitter Hamiltonian. In the framework of a suitable phase-space analysis, the correlations generated through the interaction are studied by considering a quantity proportional to the variance of difference between the detected photocurrents of all the possible couples of modes. We use this quantity to demonstrate the invariance through the interaction and the correlations swapping also in the presence of nonideal photodetection.
In general, a pair of uncorrelated Gaussian states mixed in a beam splitter (BS) produces a correlated state at the output. However, when the inputs are identical Gaussian states the output state is equal to the input, and no correlations appear, as the interference had not taken place. On the other hand, since physical phenomena do have observable effects, and the BS is there, a question arises on how to reveal the interference between the two beams. We prove theoretically and demonstrate experimentally that this is possible if at least one of the two beams is prepared in a discordant, i.e., Gaussian correlated, state with a third beam. We also apply the same technique to reveal the erasure of polarization information. Our experiment involves thermal states and the results show that Gaussian discordant states, even when they show a positive Glauber P-function, may be useful to achieve specific tasks.
Entanglement detection and quantification usually require the knowledge of correlations and thus is a global issue. For both theoretical and practical reasons, it is desirable to characterize entanglement via local quantities. Of course, this can only be achieved in special setups with some underlying structure encoding the correlations. For the often encountered bilinear interactions such as beamsplitter experiments, we propose an operational and friendly entanglement criterion for the two-mode Gaussian output states. Specifically, we show that in order to detect and evaluate the entanglement of the output states of a bilinear interaction involving uncorrelated Gaussian input states, we do not need to know the joint covariance matrix of the whole two-mode output states. Instead, we only need the respective covariances of the reduced states of the two input modes and that of the two output modes, which are all local quantities pertaining to a single mode and can be easily measured locally without explicitly considering the correlations between the modes. This is achieved by exploiting the input-output characteristics of bilinear interactions. The result recasts the celebrated entanglement criteria of Simon ( Phys. Rev. Lett. , 84 (2000) 2726) and Duan et al . ( Phys. Rev. Lett. , 84 (2000) 2722) into a more convenient and simple form.
We consider generic $(m\ifmmode\times\else\texttimes\fi{}n)$-mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n)(m+n)(m+n)-mode Gaussian states invariant under local mode permutations on the mmm-mode and nnn-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of $m+n\ensuremath{-}2$ uncorrelated single-mode states. The entanglement between the mmm-mode and the nnn-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of (m+n)(m+n)(m+n)-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes.
The behavior of general nonclassical two-mode Gaussian states at a beam splitter is investigated. Single-mode nonclassicality as well as two-mode entanglement of both input and output states are analyzed suggesting their suitable quantifiers. These quantifiers are derived from local and global invariants of linear unitary two-mode transformations such that the sum of input (or output) local nonclassicality measures and entanglement measure gives a global invariant. This invariant quantifies the global nonclassicality resource. Mutual transformations of local nonclassicalities and entanglement induced by the beam splitter are analyzed considering incident noisy twin beams, single-mode noisy squeezed vacuum states, and states encompassing both squeezed states and twin beams. A rich tapestry of interesting nonclassical output states is predicted.