LOCC distinguishability of unilaterally transformable quantum states

We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way local operations and classical communication (LOCC) where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bob's Hilbert space. We give examples of sets of N ≤ d maximally entangled states in d⊗d for d = 4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly, for d = 5,6, our examples consist of four and five states, respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.

[1]  Debbie W. Leung,et al.  Quantum data hiding , 2002, IEEE Trans. Inf. Theory.

[2]  Somshubhro Bandyopadhyay,et al.  Local Distinguishability of Any Three Quantum States , 2006 .

[3]  John Watrous,et al.  Bipartite subspaces having no bases distinguishable by local operations and classical communication. , 2005, Physical review letters.

[4]  Michael Nathanson.  Distinguishing bipartitite orthogonal states using LOCC: Best and worst cases , 2005 .

[5]  M. Murao,et al.  Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication. , 2005, Physical review letters.

[6]  A. Sen De,et al.  Distinguishability of Bell states. , 2001, Physical Review Letters.

[7]  M. Horodecki,et al.  Local indistinguishability: more nonlocality with less entanglement. , 2003, Physical review letters.

[8]  Anthony Chefles.  Condition for unambiguous state discrimination using local operations and classical communication , 2004 .

[9]  R F Werner,et al.  Hiding classical data in multipartite quantum states. , 2002, Physical review letters.

[10]  S. Bandyopadhyay.  Entanglement and perfect discrimination of a class of multiqubit states by local operations and classical communication , 2010 .

[11]  Barry C. Sanders,et al.  Erratum: Graph states for quantum secret sharing [Phys. Rev. A 78, 042309 (2008)] , 2011 .

[12]  D Cavalcanti,et al.  Distribution of entanglement in large-scale quantum networks , 2012, Reports on progress in physics. Physical Society.

[13]  Dong Yang,et al.  Optimally conclusive discrimination of nonorthogonal entangled states by local operations and classical communications , 2002 .

[14]  Lawrence Weiskrantz,et al.  Discussions and conclusions , 1998 .

[15]  Debasis Sarkar,et al.  Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement , 2002 .

[16]  D. Markham,et al.  Graph states for quantum secret sharing , 2008, 0808.1532.

[17]  Scott M. Cohen.  Local distinguishability with preservation of entanglement , 2007 .

[18]  Yuan Feng,et al.  Distinguishability of Quantum States by Separable Operations , 2007, IEEE Transactions on Information Theory.

[19]  D. Markham,et al.  Optimal local discrimination of two multipartite pure states , 2001, quant-ph/0102073.

[20]  Vedral,et al.  Local distinguishability of multipartite orthogonal quantum states , 2000, Physical review letters.

[21]  Ping Xing Chen,et al.  Orthogonality and distinguishability: Criterion for local distinguishability of arbitrary orthogonal states , 2003 .

[22]  Yuan Feng,et al.  Distinguishing arbitrary multipartite basis unambiguously using local operations and classical communication. , 2007, Physical review letters.

[23]  C. H. Bennett,et al.  Unextendible product bases and bound entanglement , 1998, quant-ph/9808030.

[24]  C. H. Bennett,et al.  Quantum nonlocality without entanglement , 1998, quant-ph/9804053.

[25]  H. Fan.  Distinguishability and indistinguishability by local operations and classical communication. , 2004, Physical review letters.

[26]  L. Hardy,et al.  Nonlocality, asymmetry, and distinguishing bipartite states. , 2002, Physical review letters.

[27]  Debasis Sarkar,et al.  Distinguishability of maximally entangled states , 2004 .

[28]  D. Leung,et al.  Hiding bits in bell states. , 2000, Physical Review Letters.