LOCC convertibility of entangled states in infinite-dimensional systems

We advance on the conversion of bipartite quantum states via local operations and classical communication (LOCC) for infinite-dimensional systems. We introduce δ-LOCC convertibility based on the observation that any pure state can be approximated by a state with finite-support Schmidt coefficients....

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Autores principales: Massri, César, Bellomo, Guido, Freytes, Hector, Giuntini, Roberto, Sergioli, Giuseppe, Bosyk, Gustavo Martín
Formato: Articulo
Lenguaje:Inglés
Publicado: 2024
Materias:
Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/167383
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SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-167383
record_format dspace
spelling I19-R120-10915-1673832024-06-19T20:08:40Z http://sedici.unlp.edu.ar/handle/10915/167383 LOCC convertibility of entangled states in infinite-dimensional systems Massri, César Bellomo, Guido Freytes, Hector Giuntini, Roberto Sergioli, Giuseppe Bosyk, Gustavo Martín 2024 2024-06-19T13:44:28Z en Física entanglement LOCC convertibility majorization lattice common resources infinite dimension We advance on the conversion of bipartite quantum states via local operations and classical communication (LOCC) for infinite-dimensional systems. We introduce δ-LOCC convertibility based on the observation that any pure state can be approximated by a state with finite-support Schmidt coefficients. We show that δ-LOCC convertibility of bipartite states is fully characterized by a majorization relation between the sequences of squared Schmidt coefficients, providing a novel extension of Nielsen’s theorem for infinite-dimensional systems. Hence, our definition is equivalent to the one of ϵ-LOCC convertibility (Owari et al 2008 Quantum Inf. Comput. 8 0030), but deals with states having finitely supported sequences of Schmidt coefficients. Additionally, we discuss the notions of optimal common resource and optimal common product in this scenario. The optimal common product always exists, whereas the optimal common resource depends on the existence of a common resource. This highlights a distinction between the resource-theoretic aspects of finite versus infinite-dimensional systems. Our results rely on the order-theoretic properties of majorization for infinite sequences, applicable beyond the LOCC convertibility problem. Instituto de Física La Plata Articulo Articulo http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
spellingShingle Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
Massri, César
Bellomo, Guido
Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
Bosyk, Gustavo Martín
LOCC convertibility of entangled states in infinite-dimensional systems
topic_facet Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
description We advance on the conversion of bipartite quantum states via local operations and classical communication (LOCC) for infinite-dimensional systems. We introduce δ-LOCC convertibility based on the observation that any pure state can be approximated by a state with finite-support Schmidt coefficients. We show that δ-LOCC convertibility of bipartite states is fully characterized by a majorization relation between the sequences of squared Schmidt coefficients, providing a novel extension of Nielsen’s theorem for infinite-dimensional systems. Hence, our definition is equivalent to the one of ϵ-LOCC convertibility (Owari et al 2008 Quantum Inf. Comput. 8 0030), but deals with states having finitely supported sequences of Schmidt coefficients. Additionally, we discuss the notions of optimal common resource and optimal common product in this scenario. The optimal common product always exists, whereas the optimal common resource depends on the existence of a common resource. This highlights a distinction between the resource-theoretic aspects of finite versus infinite-dimensional systems. Our results rely on the order-theoretic properties of majorization for infinite sequences, applicable beyond the LOCC convertibility problem.
format Articulo
Articulo
author Massri, César
Bellomo, Guido
Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
Bosyk, Gustavo Martín
author_facet Massri, César
Bellomo, Guido
Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
Bosyk, Gustavo Martín
author_sort Massri, César
title LOCC convertibility of entangled states in infinite-dimensional systems
title_short LOCC convertibility of entangled states in infinite-dimensional systems
title_full LOCC convertibility of entangled states in infinite-dimensional systems
title_fullStr LOCC convertibility of entangled states in infinite-dimensional systems
title_full_unstemmed LOCC convertibility of entangled states in infinite-dimensional systems
title_sort locc convertibility of entangled states in infinite-dimensional systems
publishDate 2024
url http://sedici.unlp.edu.ar/handle/10915/167383
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AT giuntiniroberto loccconvertibilityofentangledstatesininfinitedimensionalsystems
AT sergioligiuseppe loccconvertibilityofentangledstatesininfinitedimensionalsystems
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