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

Physical Review A

Distillation of multiple copies of Bell states

Yi-Xin Chen, Jinshuang Jin, Dong Yang

Published Jan 17, 2003• 9 citations
Publisher

Abstract

It is impossible to discriminate four Bell states through local operations and classical communication, if only one copy is provided. To complete this task, two copies will suffice and be necessary. When $2n$ copies are provided, we show that the distillable entanglement is exactly $2n\ensuremath{-}2.$ Surprisingly, when $2n\ensuremath{-}1$ copies are provided, the distillable entanglement is also $2n\ensuremath{-}2.$

DOI
10.1103/physreva.67.014302

Related papers

Distillable entanglement of multiple copies of Bell states

Yi-Xin Chen, Dong Yang

It is impossible to discriminate four Bell states through local operations and classical communication, if only one copy is provided. To complete this task, two copies will suffice and be necessary. When n copies are provided, we show that the distillable entanglement is exactly $n\ensuremath{-}2.$

arXiv:quant-ph/0204004•Physical Review A•Jul 18, 2002•12 citations

Distinguishability of Bell States

Sibasish Ghosh A, Guruprasad Kar, Anirban Roy +2 more

More than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication (LOCC) are allowed. We show that four Bell states cannot be discriminated by LOCC, even probabilistically, using the separability properties of a four-party unlockable bound entangled state. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated with certainty by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states.

arXiv:quant-ph/0106148•Physical Review Letters•Dec 13, 2001•258 citations

Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement

Sibasish Ghosh A, Guruprasad Kar, Anirban Roy +3 more

We show that the four states $a|00〉+b|11〉, \overline{b}|00〉\ensuremath{-}\ifmmode \bar{a}\else \={a}\fi{}|11〉, c|01〉+d|10〉,$ and $\overline{d}|01〉\ensuremath{-}\overline{c}|10〉$ cannot be discriminated with certainty if only local operations and classical communication (LOCC) are allowed and if only a single copy is provided, except in the case when they are simply $|00〉, |11〉, |01〉,$ and $|10〉$ (in which case they are trivially distinguishable with LOCC). We go on to show that there exists a continuous range of values of $a, b, c,$ and d such that even three states among the above four are not locally distinguishable, if only a single copy is provided. The proof follows from the fact that logarithmic negativity is an upper bound of distillable entanglement.

arXiv:quant-ph/0111136•Physical Review A•Jun 4, 2002•43 citations

Bell-pair distillation under imperfect operations

András Kinyó, Tamás Kiss, Orsolya Kálmán

We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.

quant-pharXiv:2610.35699•Oct 27, 2026•0 citations

Local cloning of Bell states and distillable entanglement

Sibasish Ghosh A, Guruprasad Kar, Anirban Roy

The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result we provide here some additional examples of reversible as well as irreversible states.

arXiv:quant-ph/0311062•Physical Review A•May 13, 2004•22 citations

Gaussian Transformations and Distillation of Entangled Gaussian States

Jaromı́r Fiurášek

We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [preceding Letter, Phys. Rev. Lett. 89, 137903 ()]] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.

arXiv:quant-ph/0204069•Physical Review Letters•Sep 4, 2002•411 citations
It is impossible to discriminate four Bell states through local operations and classical communication, if only one copy is provided. To complete this task, two copies will suffice and be necessary. When 2n2n2n copies are provided, we show that the distillable entanglement is exactly 2n\ensuremath−2.2n\ensuremath{-}2.2n\ensuremath−2. Surprisingly, when 2n\ensuremath−12n\ensuremath{-}12n\ensuremath−1 copies are provided, the distillable entanglement is also 2n\ensuremath−2.2n\ensuremath{-}2.2n\ensuremath−2.
More than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication (LOCC) are allowed. We show that four Bell states cannot be discriminated by LOCC, even probabilistically, using the separability properties of a four-party unlockable bound entangled state. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated with certainty by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states.
We show that the four states $a|00〉+b|11〉, \overline{b}|00〉\ensuremath{-}\ifmmode \bar{a}\else \={a}\fi{}|11〉, c|01〉+d|10〉,$ and $\overline{d}|01〉\ensuremath{-}\overline{c}|10〉$ cannot be discriminated with certainty if only local operations and classical communication (LOCC) are allowed and if only a single copy is provided, except in the case when they are simply ∣00〉,∣11〉,∣01〉,|00〉, |11〉, |01〉,∣00〉,∣11〉,∣01〉, and ∣10〉|10〉∣10〉 (in which case they are trivially distinguishable with LOCC). We go on to show that there exists a continuous range of values of a,b,c,a, b, c,a,b,c, and d such that even three states among the above four are not locally distinguishable, if only a single copy is provided. The proof follows from the fact that logarithmic negativity is an upper bound of distillable entanglement.
We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.
We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [preceding Letter, Phys. Rev. Lett. 89, 137903 ()]] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.