Limitations to sharing entanglement

We discuss limitations to sharing entanglement known as monogamy of entanglement. Our pedagogical approach commences with simple examples of limited entanglement sharing for pure three-qubit states and progresses to the more general case of mixed-state monogamy relations with multiple qudits.

[1]  Frank Verstraete,et al.  Local vs. joint measurements for the entanglement of assistance , 2003, Quantum Inf. Comput..

[2]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[3]  A. Zeilinger,et al.  Going Beyond Bell’s Theorem , 2007, 0712.0921.

[4]  V. Vedral,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

[5]  A. Winter,et al.  Monogamy of quantum entanglement and other correlations , 2003, quant-ph/0310037.

[6]  Jeong San Kim Tsallis entropy and entanglement constraints in multiqubit systems , 2009, 0911.5181.

[7]  Yong-Cheng Ou,et al.  Violation of monogamy inequality for higher-dimensional objects , 2006, quant-ph/0612127.

[8]  M. Lewenstein,et al.  Volume of the set of separable states , 1998, quant-ph/9804024.

[9]  M. Plenio,et al.  Quantifying Entanglement , 1997, quant-ph/9702027.

[10]  W. Wootters,et al.  Distributed Entanglement , 1999, quant-ph/9907047.

[11]  W. Wootters Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[12]  Barry C. Sanders,et al.  Dual monogamy inequality for entanglement , 2007 .

[13]  M. Plenio,et al.  Teleportation, entanglement and thermodynamics in the quantum world , 1998 .

[14]  F. Verstraete,et al.  General monogamy inequality for bipartite qubit entanglement. , 2005, Physical review letters.

[15]  Jeong San Kim,et al.  Generalized W-class state and its monogamy relation , 2008, 0805.1690.

[16]  Mário Ziman,et al.  Programmable Quantum Gate Arrays , 2001 .

[17]  M. Fannes,et al.  Symmetric states of composite systems , 1988 .

[18]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[19]  J. Neumann Mathematische grundlagen der Quantenmechanik , 1935 .

[20]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[21]  Sevag Gharibian,et al.  Strong NP-hardness of the quantum separability problem , 2008, Quantum Inf. Comput..

[22]  Guifre Vidal Entanglement monotones , 1998, quant-ph/9807077.

[23]  A. Winter,et al.  “Squashed entanglement”: An additive entanglement measure , 2003, quant-ph/0308088.

[24]  Leonid Gurvits,et al.  Classical complexity and quantum entanglement , 2004, J. Comput. Syst. Sci..

[25]  Jeong San Kim,et al.  Polygamy of distributed entanglement , 2009, 0903.4413.

[26]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

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

[28]  F. Brandão,et al.  Faithful Squashed Entanglement , 2010, 1010.1750.

[29]  Elham Kashefi,et al.  The One Way to Quantum Computation , 2006, ICALP.

[30]  M. Dušek,et al.  Experimental realization of a programmable quantum gate , 2008, 0812.1457.

[31]  A. O. Pittenger,et al.  Convexity and the separability problem of quantum mechanical density matrices , 2001, quant-ph/0103038.

[32]  Jeong San Kim General polygamy inequality of multiparty quantum entanglement , 2012, 1202.2184.

[33]  Barbara M. Terhal Is entanglement monogamous? , 2004, IBM J. Res. Dev..

[34]  C. Adami,et al.  Negative entropy and information in quantum mechanics , 1995, quant-ph/9512022.

[35]  Travis Norsen,et al.  Bell's theorem , 2011, Scholarpedia.

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

[37]  Jeong San Kim,et al.  Monogamy of multi-qubit entanglement using Rényi entropy , 2009, 0911.5180.

[38]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[39]  N. Gisin,et al.  General properties of nonsignaling theories , 2005, quant-ph/0508016.

[40]  R. Werner,et al.  Quantum Statistical Mechanics of General Mean Field Systems , 1989 .

[41]  M. Horodecki,et al.  Separability of mixed states: necessary and sufficient conditions , 1996, quant-ph/9605038.

[42]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[43]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[44]  Vlatko Vedral,et al.  Entanglement in Quantum Information Theory , 1998, quant-ph/9804075.

[45]  G. Vidal On the characterization of entanglement , 1998 .

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

[47]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[48]  Barry C. Sanders,et al.  Bounds on general entropy measures , 2003 .

[49]  V. Buzek,et al.  Approximate programmable quantum processors , 2005, quant-ph/0510161.