# Bound on local unambiguous discrimination between multipartite quantum states

Bound on local unambiguous discrimination between multipartite quantum states We investigate the upper bound on unambiguous discrimination by local operations and classical communication. We demonstrate that any set of linearly independent multipartite pure quantum states can be locally unambiguously discriminated if the number of states in the set is no more than $$\max \{d_{i}\}$$ max { d i } , where the space spanned by the set can be expressed in the irreducible form $$\otimes _{i=1}^{N}d_{i}$$ ⊗ i = 1 N d i and $$d_{i}$$ d i is the optimal local dimension of the $$i\hbox {th}$$ i th party. That is, $$\max \{d_{i}\}$$ max { d i } is an upper bound. We also show that it is tight, namely there exists a set of $$\max \{d_{i}\}+1$$ max { d i } + 1 states, in which at least one of the states cannot be locally unambiguously discriminated. Our result gives the reason why the multiqubit system is the only exception when any three quantum states are locally unambiguously distinguished. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Bound on local unambiguous discrimination between multipartite quantum states

, Volume 14 (2) – Nov 12, 2014
7 pages

/lp/springer_journal/bound-on-local-unambiguous-discrimination-between-multipartite-quantum-FklOvdTQIi
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/s11128-014-0870-3
Publisher site
See Article on Publisher Site

### Abstract

We investigate the upper bound on unambiguous discrimination by local operations and classical communication. We demonstrate that any set of linearly independent multipartite pure quantum states can be locally unambiguously discriminated if the number of states in the set is no more than $$\max \{d_{i}\}$$ max { d i } , where the space spanned by the set can be expressed in the irreducible form $$\otimes _{i=1}^{N}d_{i}$$ ⊗ i = 1 N d i and $$d_{i}$$ d i is the optimal local dimension of the $$i\hbox {th}$$ i th party. That is, $$\max \{d_{i}\}$$ max { d i } is an upper bound. We also show that it is tight, namely there exists a set of $$\max \{d_{i}\}+1$$ max { d i } + 1 states, in which at least one of the states cannot be locally unambiguously discriminated. Our result gives the reason why the multiqubit system is the only exception when any three quantum states are locally unambiguously distinguished.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 12, 2014

### References

• Distinguishability of quantum states by separable operations
Duan, R; Feng, Y; Xin, Y; Ying, M
• Characterizing locally indistinguishable orthogonal product states
Feng, Y; Shi, Y
• When do local operations and classical communication suffice for two-qubit state discrimination?
Chitambar, E; Duan, R; Hsieh, MH

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