Entanglement as a resource for local state discrimination in multipartite systems

We explore the question of using an entangled state as a universal resource for implementing quantum measurements by local operations and classical communication (LOCC). We show that for most systems consisting of three or more subsystems, there is no entangled state from the same space that can enable all measurements by LOCC. This is in direct contrast to the bipartite case, where a maximally entangled state is an universal resource. Our results are obtained showing an equivalence between the problem of local state transformation and that of entanglement-assisted local unambiguous state discrimination.

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

[2]  J. Cirac,et al.  Entangling operations and their implementation using a small amount of entanglement. , 2000, Physical review letters.

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

[4]  N. Wallach,et al.  Classification of multipartite entanglement of all finite dimensionality. , 2013, Physical review letters.

[5]  Somshubhro Bandyopadhyay,et al.  Entanglement cost of nonlocal measurements , 2008, 0809.2264.

[6]  E Bagan,et al.  Local discrimination of mixed States. , 2010, Physical review letters.

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

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

[9]  Massar,et al.  Optimal extraction of information from finite quantum ensembles. , 1995, Physical review letters.

[10]  N. Wallach,et al.  Necessary and sufficient conditions for local manipulation of multipartite pure quantum states , 2011, 1103.5096.

[11]  Somshubhro Bandyopadhyay,et al.  LOCC distinguishability of unilaterally transformable quantum states , 2011, 1102.0841.

[12]  J. Eisert,et al.  Schmidt measure as a tool for quantifying multiparticle entanglement , 2000, quant-ph/0007081.

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

[14]  Somshubhro Bandyopadhyay,et al.  Entanglement cost of two-qubit orthogonal measurements , 2010, 1005.5236.

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

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

[17]  J. Cirac,et al.  Three qubits can be entangled in two inequivalent ways , 2000, quant-ph/0005115.

[18]  M. Ying,et al.  Four locally indistinguishable ququad-ququad orthogonal maximally entangled states. , 2011, Physical review letters.

[19]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[20]  R. Duan,et al.  Common Resource State for Preparing Multipartite Quantum Systems via Local Operations and Classical Communication , 2016, 1601.06220.

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

[22]  Somshubhro Bandyopadhyay,et al.  More nonlocality with less purity. , 2011, Physical review letters.

[23]  B. Kraus,et al.  The MES of tripartite qutrit states and pure state separable transformations which are not possible via LOCC , 2015, 1511.03158.

[24]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

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

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

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

[28]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[29]  Anthony Chefles,et al.  Unambiguous discrimination between linearly independent quantum states , 1998, quant-ph/9807022.

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

[31]  Scott M. Cohen.  Understanding entanglement as resource: locally distinguishing unextendible product bases , 2007, 0708.2396.

[32]  P. Shor,et al.  Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement , 1999, quant-ph/9908070.

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

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

[35]  M. Murao,et al.  Direct evaluation of pure graph state entanglement , 2012, 1207.5877.

[36]  Noah Linden,et al.  Nonlocal content of quantum operations , 2001 .

[37]  W. Wootters,et al.  Optimal detection of quantum information. , 1991, Physical review letters.

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

[39]  Dominic W. Berry.  Implementation of multipartite unitary operations with limited resources , 2007 .

[40]  M. Plenio,et al.  Entanglement-Assisted Local Manipulation of Pure Quantum States , 1999, quant-ph/9905071.

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

[42]  Runyao Duan,et al.  Tensor rank and stochastic entanglement catalysis for multipartite pure states. , 2010, Physical review letters.

[43]  A. Winter,et al.  Distinguishability of Quantum States Under Restricted Families of Measurements with an Application to Quantum Data Hiding , 2008, 0810.2327.

[44]  Somshubhro Bandyopadhyay,et al.  Limitations on Separable Measurements by Convex Optimization , 2014, IEEE Transactions on Information Theory.

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

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

[47]  J. Eisert,et al.  Multiparty entanglement in graph states , 2003, quant-ph/0307130.