One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension $d\ge4$ . We show that every set of $k$ pairwise orthogonal maximally entangled states in $\mathbb C^d\otimes\mathbb C^d$ is perfectly distinguishable by an $A\to B\to A$ protocol whenever $d\ge Ck^4[\log(2k)]^ν$ , for universal constants $C,ν>0$ . A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to $Ω\!\left(d^{1/4}/(\log d)^{ν/4}\right)$ , establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension $d\ge4$. We show that every set of $k$ pairwise orthogonal maximally entangled states in $\mathbb C^d\otimes\mathbb C^d$ is perfectly distinguishable by an $A\to B\to A$ protocol whenever $d\ge Ck^4[\log(2k)]^ν$, for universal constants $C,ν>0$. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to $Ω\!\left(d^{1/4}/(\log d)^{ν/4}\right)$, establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.

quant-pharXiv:2610.04288Oct 6, 20260 citations

Constructions of locally distinguishable sets of maximally entangled states which require two-way LOCC

Jiangtao Yuan, Ying‐Hui Yang, Caihong Wang

Abstract Most of known locally distinguishable sets of maximally entangled states (MESs) can be perfectly distinguished with one-way local operations and classical communication (1-LOCC), and there are not many known locally distinguishable sets which require two-way LOCC (2-LOCC). Recently some such sets of MESs have been built, that is, they can be locally distinguished only with 2-LOCC. In this work, we show that there exist a lot of locally distinguishable MESs which require 2-LOCC (denote such sets by 2-LOCC sets). Firstly generalized Bell states are employed to construct lots of 1-LOCC indistinguishable sets of MESs in the quantum systems C a + ( a + 1 ) r ⊗ C a + ( a + 1 ) r and C a + ( a + 2 ) r ⊗ C a + ( a + 2 ) r . Then we build a lot of 2-LOCC sets by using Weyl commutation relation and two constructive methods. Especially, it is shown that there are at least 8 and 105 2-LOCC sets in quantum systems C 10 ⊗ C 10 and C 19 ⊗ C 19 respectively.Abstract Most of known locally distinguishable sets of maximally entangled states (MESs) can be perfectly distinguished with one-way local operations and classical communication (1-LOCC), and there are not many known locally distinguishable sets which require two-way LOCC (2-LOCC). Recently some such sets of MESs have been built, that is, they can be locally distinguished only with 2-LOCC. In this work, we show that there exist a lot of locally distinguishable MESs which require 2-LOCC (denote such sets by 2-LOCC sets). Firstly generalized Bell states are employed to construct lots of 1-LOCC indistinguishable sets of MESs in the quantum systems C a + ( a + 1 ) r ⊗ C a + ( a + 1 ) r and C a + ( a + 2 ) r ⊗ C a + ( a + 2 ) r . Then we build a lot of 2-LOCC sets by using Weyl commutation relation and two constructive methods. Especially, it is shown that there are at least 8 and 105 2-LOCC sets in quantum systems C 10 ⊗ C 10 and C 19 ⊗ C 19 respectively.

Journal of Physics A Mathematical and TheoreticalOct 23, 202010 citations

Three maximally entangled states can require two-way local operations and classical communication for local discrimination

Michael Nathanson

We show that there exist sets of three mutually orthogonal $d$ -dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of $d$ . This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal $d$ -dimensional maximally entangled states can be perfectly distinguished using measurements with a positive partial transpose (PPT) and can be distinguished with one-way LOCC with high probability. These results circle around the question of whether there exist three maximally entangled states which cannot be distinguished using the full power of LOCC; we discuss possible approaches to answer this question.We show that there exist sets of three mutually orthogonal $d$-dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of $d$. This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal $d$-dimensional maximally entangled states can be perfectly distinguished using measurements with a positive partial transpose (PPT) and can be distinguished with one-way LOCC with high probability. These results circle around the question of whether there exist three maximally entangled states which cannot be distinguished using the full power of LOCC; we discuss possible approaches to answer this question.

arXiv:1310.4220Physical Review ADec 12, 201369 citations

Local distinguishability of maximally entangled states in canonical form

Zhichao Zhang, Fei Gao, Su‐Juan Qin +2 more

Quantum Information ProcessingAug 14, 20155 citations

One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension

d\ge4

. We show that every set of

k

pairwise orthogonal maximally entangled states in

\mathbb C^d\otimes\mathbb C^d

is perfectly distinguishable by an

A\to B\to A

protocol whenever

d\ge Ck^4[\log(2k)]^ν

, for universal constants

C,ν>0

. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to

Ω\!\left(d^{1/4}/(\log d)^{ν/4}\right)

, establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.

We show that there exist sets of three mutually orthogonal

d

-dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of

d

. This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal

d

-dimensional maximally entangled states can be perfectly distinguished using measurements with a positive partial transpose (PPT) and can be distinguished with one-way LOCC with high probability. These results circle around the question of whether there exist three maximally entangled states which cannot be distinguished using the full power of LOCC; we discuss possible approaches to answer this question.