# One-way LOCC indistinguishability of maximally entangled states

One-way LOCC indistinguishability of maximally entangled states In this letter, we mainly study the local indistinguishability of mutually orthogonal maximally entangled states, which are in canonical form. Firstly, we present a feasible sufficient and necessary condition for distinguishing such states by one-way local operations and classical communication (LOCC). Secondly, for the application of this condition, we exhibit one class of maximally entangled states that can be locally distinguished with certainty. Furthermore, sets of $$d-1$$ d - 1 indistinguishable maximally entangled states by one-way LOCC are demonstrated in $$d \otimes d$$ d ⊗ d (for $$d=7, 8, 9, 10$$ d = 7 , 8 , 9 , 10 ). Interestingly, we discover there exist sets of $$d-2$$ d - 2 such states in $$d \otimes d$$ d ⊗ d (for $$d=8, 9, 10$$ d = 8 , 9 , 10 ), which are not perfectly distinguishable by one-way LOCC. Finally, we conjecture that there exist $$d-1$$ d - 1 or fewer indistinguishable maximally entangled states in $$d \otimes d(d \ge 5)$$ d ⊗ d ( d ≥ 5 ) by one-way LOCC. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# One-way LOCC indistinguishability of maximally entangled states

, Volume 13 (3) – Nov 24, 2013
10 pages

/lp/springer_journal/one-way-locc-indistinguishability-of-maximally-entangled-states-6qJyjkxBnL
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0691-9
Publisher site
See Article on Publisher Site

### Abstract

In this letter, we mainly study the local indistinguishability of mutually orthogonal maximally entangled states, which are in canonical form. Firstly, we present a feasible sufficient and necessary condition for distinguishing such states by one-way local operations and classical communication (LOCC). Secondly, for the application of this condition, we exhibit one class of maximally entangled states that can be locally distinguished with certainty. Furthermore, sets of $$d-1$$ d - 1 indistinguishable maximally entangled states by one-way LOCC are demonstrated in $$d \otimes d$$ d ⊗ d (for $$d=7, 8, 9, 10$$ d = 7 , 8 , 9 , 10 ). Interestingly, we discover there exist sets of $$d-2$$ d - 2 such states in $$d \otimes d$$ d ⊗ d (for $$d=8, 9, 10$$ d = 8 , 9 , 10 ), which are not perfectly distinguishable by one-way LOCC. Finally, we conjecture that there exist $$d-1$$ d - 1 or fewer indistinguishable maximally entangled states in $$d \otimes d(d \ge 5)$$ d ⊗ d ( d ≥ 5 ) by one-way LOCC.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 24, 2013

### References

• Positive-partial-transpose-indistinguishable states via semidefinite programming
Cosentino, A

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