THEORETICAL AND EXPERIMENTAL ASPECTS OF QUANTUM DISCORD AND RELATED MEASURES

Correlations are a very important tool in the study of multipartite systems, for both classical and quantum ones. The discussion about the quantum nature of correlations permeates Physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Here, we provide a short review about the quantum nature of correlations, discussing both its theoretical and experimental aspects. We focus on quantum discord and related measures. After discussing their fundamental aspects (theoretically and experimentally), we proceed by analysing the dynamical behavior of correlations under decoherence as well as some applications in different scenarios, such as quantum computation and relativity, passing through critical and biological systems.

[1]  Graham R. Fleming,et al.  Two-dimensional spectroscopy of electronic couplings in photosynthesis , 2005, Nature.

[2]  R. Serra,et al.  Sudden change in quantum and classical correlations and the Unruh effect , 2010, 1003.4477.

[3]  Joshua A. Slater,et al.  An experimental test of all theories with predictive power beyond quantum theory , 2011, 1105.0133.

[4]  R. Laflamme,et al.  Experimental detection of nonclassical correlations in mixed-state quantum computation , 2011, 1105.2262.

[5]  Raoul Dillenschneider,et al.  Quantum discord and quantum phase transition in spin chains , 2008, 0809.1723.

[6]  A. Acín,et al.  Almost all quantum states have nonclassical correlations , 2009, 0908.3157.

[7]  Atsushi Higuchi,et al.  The Unruh effect and its applications , 2007, 0710.5373.

[8]  Robabeh Rahimi,et al.  Single-experiment-detectable nonclassical correlation witness , 2009, 0911.3460.

[9]  J. Piilo,et al.  Sudden transition between classical and quantum decoherence. , 2010, Physical review letters.

[10]  E. Sudarshan,et al.  Completely positive maps and classical correlations , 2007, quant-ph/0703022.

[11]  A. Rau,et al.  Quantum discord for two-qubit X states , 2010, 1002.3429.

[12]  MAXWELL’S DEMONS,et al.  Quantum Discord and Maxwell's Demons , 2002 .

[13]  D. Chruściński,et al.  Witnessing quantum discord in 2 x N systems , 2010, 1004.0434.

[14]  Chengjie Zhang,et al.  Witnessing the quantum discord of all the unknown states , 2011, 1102.4710.

[15]  M. Schlosshauer Decoherence, the measurement problem, and interpretations of quantum mechanics , 2003, quant-ph/0312059.

[16]  Shuangshuang Fu,et al.  Measurement-induced nonlocality. , 2011, Physical review letters.

[17]  J. Oppenheim,et al.  Thermodynamical approach to quantifying quantum correlations. , 2001, Physical review letters.

[18]  Gerd Leuchs,et al.  Quantum information with continuous variables of atoms and light , 2007 .

[19]  A. Toor,et al.  Quantum Games and Quantum Discord , 2010, 1012.1428.

[20]  E. Mirman,et al.  The Einstein-Podolsky-Rosen paradox , 1973 .

[21]  Ladislav Mista,et al.  Gaussian localizable entanglement , 2007 .

[22]  Guo‐Feng Zhang,et al.  Measurement-induced disturbance and thermal entanglement in spin models , 2011, 1101.5512.

[23]  G. Guo,et al.  Quantum correlation and classical correlation dynamics in the spin-boson model , 2010, 1007.0669.

[24]  E. Schrödinger Discussion of Probability Relations between Separated Systems , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[25]  Masato Koashi,et al.  ‘Quantum Nonlocality without Entanglement’ in a Pair of Qubits , 2007, OSA Workshop on Entanglement and Quantum Decoherence.

[26]  A. R. P. Rau,et al.  Calculation of quantum discord for qubit-qudit or N qubits , 2011, 1106.4488.

[27]  M. S. Sarandy Classical correlation and quantum discord in critical systems , 2009, 0905.1347.

[28]  S. Sachdev Quantum Phase Transitions , 1999 .

[29]  Animesh Datta,et al.  A Condition for the Nullity of Quantum Discord , 2010, 1003.5256.

[30]  Tal Mor,et al.  "Quantumness" versus "Classicality" of Quantum States , 2007 .

[31]  Gerardo Adesso,et al.  CHARACTERIZING QUANTUMNESS VIA ENTANGLEMENT CREATION , 2011, 1105.3419.

[32]  G. Rigolin,et al.  Quantum correlations in spin chains at finite temperatures and quantum phase transitions. , 2010, Physical review letters.

[33]  G. Mahler,et al.  Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems , 2004 .

[34]  Aurelian Isar,et al.  Quantum Entanglement and Quantum Discord of Two-Mode Gaussian States in a Thermal Environment , 2011, Open Syst. Inf. Dyn..

[35]  P. Horodecki,et al.  No-local-broadcasting theorem for multipartite quantum correlations. , 2007, Physical review letters.

[36]  Relation between “no broadcasting” for noncommuting states and “no local broadcasting” for quantum correlations , 2009 .

[37]  Matthias D. Lang,et al.  Quantum discord and the geometry of Bell-diagonal states. , 2010, Physical review letters.

[38]  Witness to detect quantum correlation of bipartite states in arbitrary dimension , 2011, 1104.0299.

[39]  Shunlong Luo,et al.  Observable Correlations in Two-Qubit States , 2009 .

[40]  Gustavo Rigolin,et al.  Thermal and magnetic quantum discord in Heisenberg models , 2009, 0911.3903.

[41]  Davide Rossini,et al.  Ground-state factorization and correlations with broken symmetry , 2010, 1012.4270.

[42]  M. S. Sarandy,et al.  Global quantum discord in multipartite systems , 2011, 1105.2548.

[43]  J. Cirac,et al.  Characterization of Gaussian operations and distillation of Gaussian states , 2002, quant-ph/0204085.

[44]  Charles H. Bennett,et al.  Postulates for measures of genuine multipartite correlations , 2008, 0805.3060.

[45]  H. Imai,et al.  Sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment. , 2010, Physical review letters.

[46]  Andreas Winter,et al.  Partial quantum information , 2005, Nature.

[47]  Lei Wang,et al.  A new criterion for zero quantum discord , 2011, 1102.5249.

[48]  U. Sen,et al.  Quantum discord surge heralds entanglement revival in an infinite spin chain , 2010, 1011.5309.

[49]  A. Winter,et al.  Quantum, classical, and total amount of correlations in a quantum state , 2004, quant-ph/0410091.

[50]  Davide Girolami,et al.  Measurement-induced disturbances and nonclassical correlations of Gaussian states , 2010, 1012.4302.

[51]  Markus Tiersch,et al.  A critical view on transport and entanglement in models of photosynthesis , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[52]  Č. Brukner,et al.  Necessary and sufficient condition for nonzero quantum discord. , 2010, Physical review letters.

[53]  Roberta Zambrini,et al.  Maximally discordant mixed states of two qubits , 2010, 1007.2174.

[54]  L. Davidovich,et al.  Quantum correlations as precursors of entanglement , 2010, 1008.3866.

[55]  L. Nie,et al.  Classical correlation and quantum discord mediated by cavity in two coupled qubits , 2011 .

[56]  I. S. Oliveira,et al.  Experimentally witnessing the quantumness of correlations. , 2011, Physical review letters.

[57]  M. S. Sarandy,et al.  Long-range quantum discord in critical spin systems , 2010, 1012.5926.

[58]  T. Mančal,et al.  Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems , 2007, Nature.

[59]  Giuseppe Vallone,et al.  Extremal quantum correlations: Experimental study with two-qubit states , 2011 .

[60]  L. Brillouin Maxwell's Demon Cannot Operate: Information and Entropy. I , 1951 .

[61]  S. Fei,et al.  Quantum Discord and Geometry for a Class of Two-qubit States , 2011, 1104.1843.

[62]  E. Knill,et al.  Power of One Bit of Quantum Information , 1998, quant-ph/9802037.

[63]  S. Olivares,et al.  Nonclassical correlations in non-Markovian continuous-variable systems , 2010, 1005.1043.

[64]  Animesh Datta,et al.  Role of quantum discord in quantum communication a , 2011 .

[65]  Ali S. M. Hassan,et al.  Geometric measure of quantum discord for an arbitrary state of a bipartite quantum system , 2010 .

[66]  Johan Aberg,et al.  The thermodynamic meaning of negative entropy , 2011, Nature.

[67]  Zhengmin Zhang,et al.  Quantumness of bipartite states in terms of conditional entropies , 2007 .

[68]  S. Campbell,et al.  Propagation of nonclassical correlations across a quantum spin chain , 2011, 1105.5548.

[69]  Rafael Chaves,et al.  Noisy One-Way Quantum Computations: The Role of Correlations , 2010, 1007.2165.

[70]  Animesh Datta,et al.  Interpreting quantum discord through quantum state merging , 2010, ArXiv.

[71]  I. Devetak,et al.  Distilling common randomness from bipartite quantum states , 2003, IEEE Transactions on Information Theory.

[72]  Animesh Datta,et al.  Quantum discord and the power of one qubit. , 2007, Physical review letters.

[73]  V. Vedral Ju n 20 09 The elusive source of quantum effectiveness , 2009 .

[74]  Ali S. M. Hassan,et al.  Thermal quantum and classical correlations in a two-qubit XX model in a nonuniform external magnetic field , 2010, 1007.3169.

[75]  Jyrki Piilo,et al.  Witness for initial system-environment correlations in open-system dynamics , 2010, 1004.2184.

[76]  V. Vedral The role of relative entropy in quantum information theory , 2001, quant-ph/0102094.

[77]  J. Piilo,et al.  FROZEN DISCORD IN NON-MARKOVIAN DEPHASING CHANNELS , 2010, 1006.1805.

[78]  Bo Wang,et al.  Non-Markovian effect on the quantum discord , 2009, 0911.1845.

[79]  V. Vedral Classical correlations and entanglement in quantum measurements. , 2002, Physical review letters.

[80]  W. Zurek,et al.  Quantum discord: a measure of the quantumness of correlations. , 2001, Physical review letters.

[81]  Barbara Synak-Radtke,et al.  Can quantum correlations be completely quantum? , 2007, 0705.1370.

[82]  L. Aolita,et al.  QUANTUM LOCKING OF CLASSICAL CORRELATIONS AND QUANTUM DISCORD OF CLASSICAL-QUANTUM STATES , 2011, 1105.2768.

[83]  S. Rana,et al.  Entanglement and discord of the superposition of Greenberger-Horne-Zeilinger states , 2009, 0909.4443.

[84]  Franco Nori,et al.  Colloquium: The physics of Maxwell's demon and information , 2007, 0707.3400.

[85]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[86]  F. F. Fanchini,et al.  Robustness of quantum discord to sudden death , 2009, 0905.3376.

[87]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[88]  Xiao-Ming Lu,et al.  Optimal measurements to access classical correlations of two-qubit states , 2010, 1009.1476.

[89]  Johan Aberg,et al.  The thermodynamic meaning of negative entropy , 2010, Nature.

[90]  T. Paterek,et al.  Unified view of quantum and classical correlations. , 2009, Physical review letters.

[91]  Daniel A. Lidar,et al.  Vanishing quantum discord is necessary and sufficient for completely positive maps. , 2008, Physical review letters.

[92]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

[93]  I. S. Oliveira,et al.  Environment-induced sudden transition in quantum discord dynamics. , 2011, Physical review letters.

[94]  Sixia Yu,et al.  Quantum discord of two-qubit X states , 2011, 1102.0181.

[95]  M. Paris,et al.  Gaussian quantum discord. , 2010, Physical review letters.

[96]  Hermann Kampermann,et al.  Linking quantum discord to entanglement in a measurement. , 2010, Physical review letters.

[97]  S. Luo,et al.  Geometric measure of quantum discord , 2010 .

[98]  Animesh Datta,et al.  Signatures of nonclassicality in mixed-state quantum computation , 2008, 0811.4003.

[99]  Heng Fan,et al.  Correlations in the Grover search , 2009, 0904.2703.

[100]  Zhao-Yu Sun,et al.  Quantum discord in matrix product systems , 2010 .

[101]  Aharon Brodutch,et al.  Entanglement, discord, and the power of quantum computation , 2010, 1009.2571.

[102]  S. Luo Quantum discord for two-qubit systems , 2008 .

[103]  R. M. Serra,et al.  Symmetry aspects of quantum discord , 2010, 1004.2082.

[104]  N. J. Cerf,et al.  Multipartite nonlocality without entanglement in many dimensions , 2006 .

[105]  R. Rossignoli,et al.  Quantum discord in finite XY chains , 2010, 1105.0027.

[106]  D. O. Soares-Pinto,et al.  Nonclassical correlation in NMR quadrupolar systems , 2010, 1004.0022.

[107]  M. Horodecki,et al.  Quantum entanglement , 2007, quant-ph/0702225.

[108]  Nan Li,et al.  Classical states versus separable states , 2008 .

[109]  Francesco Petruccione,et al.  The Theory of Open Quantum Systems , 2002 .

[110]  Lin Chen,et al.  Detecting multipartite classical states and their resemblances , 2010, 1005.4348.

[111]  Bryan Eastin Simulating Concordant Computations , 2010 .

[112]  F. F. Fanchini,et al.  Entanglement irreversibility from quantum discord and quantum deficit. , 2010, Physical review letters.

[113]  B. Lanyon,et al.  Experimental quantum computing without entanglement. , 2008, Physical review letters.

[114]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[115]  L. Kuang,et al.  Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence , 2010, 1005.4204.

[116]  L. Aolita,et al.  Operational interpretations of quantum discord , 2010, 1008.3205.

[117]  Animesh Datta Quantum discord between relatively accelerated observers , 2009 .

[118]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

[119]  Daniel A. Lidar,et al.  Maps for general open quantum systems and a theory of linear quantum error correction , 2009, 0902.2478.

[120]  A. Datta Studies on the Role of Entanglement in Mixed-state Quantum Computation , 2008, 0807.4490.

[121]  M. Horodecki,et al.  Quantum information can be negative , 2005, quant-ph/0505062.

[122]  Davide Girolami,et al.  Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states , 2010, 1008.4136.

[123]  M. Partovi,et al.  Correlative capacity of composite quantum states. , 2009, Physical review letters.

[124]  Gregory D. Scholes,et al.  Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature , 2010, Nature.

[125]  V. Vedral,et al.  Classical and quantum correlations under decoherence , 2009, 0905.3396.

[126]  Aharon Brodutch,et al.  Quantum discord, local operations, and Maxwell's demons , 2010 .

[127]  A. Datta,et al.  Quantum versus classical correlations in Gaussian states. , 2010, Physical review letters.

[128]  Eric Lutz,et al.  Energetics of quantum correlations , 2008, 0803.4067.

[129]  T. Yu,et al.  Finite-time disentanglement via spontaneous emission. , 2004, Physical review letters.

[130]  R. M. Serra,et al.  Quantum and classical thermal correlations in the XY spin-(1/2) chain , 2010, 1002.3906.

[131]  G. Adesso,et al.  Quantum discord for general two-qubit states: Analytical progress , 2011, 1103.3189.

[132]  Gerardo Adesso,et al.  All nonclassical correlations can be activated into distillable entanglement. , 2011, Physical review letters.

[133]  A. Plastino,et al.  Properties of a geometric measure for quantum discord , 2011, 1103.0704.

[134]  G. Guo,et al.  Experimental investigation of classical and quantum correlations under decoherence. , 2009, Nature communications.

[135]  L. Nie,et al.  Classical correlation, quantum discord and entanglement for two-qubit system subject to heat bath , 2011 .

[136]  Gerardo Adesso,et al.  Continuous-variable entanglement sharing in noninertial frames , 2007, quant-ph/0701074.

[137]  Jieci Wang,et al.  Classical correlation and quantum discord sharing of Dirac fields in noninertial frames , 2009, 0912.4129.

[138]  R. Renner,et al.  Quantum theory cannot be extended , 2010 .

[139]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[140]  Daniel F. V. James,et al.  Comparison of the attempts of quantum discord and quantum entanglement to capture quantum correlations , 2010, 1007.1814.

[141]  Schumacher,et al.  Noncommuting mixed states cannot be broadcast. , 1995, Physical review letters.

[142]  Lov K. Grover Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[143]  S. Luo,et al.  Decorrelating capabilities of operations with application to decoherence , 2010 .

[144]  Nan Li,et al.  Total versus quantum correlations in quantum states , 2007 .

[145]  Сепарабельность и запутывание в состояниях систем из трех частей@@@Separability and entanglement in tripartite states , 2009 .

[146]  Vlatko Vedral,et al.  Unification of quantum and classical correlations and quantumness measures , 2011, 1104.1520.

[147]  Daniel R. Terno,et al.  Quantum Information and Relativity Theory , 2002, quant-ph/0212023.

[148]  S. Sachdev Quantum Phase Transitions , 1999 .

[149]  F. F. Fanchini,et al.  System-reservoir dynamics of quantum and classical correlations , 2009, 0910.5711.

[150]  F. F. Fanchini,et al.  Entanglement versus quantum discord in two coupled double quantum dots , 2009, 0912.1468.

[151]  F. F. Fanchini,et al.  Non-Markovian dynamics of quantum discord , 2009, 0911.1096.

[152]  F. F. Fanchini,et al.  Conservation law for distributed entanglement of formation and quantum discord , 2010, 1006.2460.

[153]  S. Luo Using measurement-induced disturbance to characterize correlations as classical or quantum , 2008 .

[154]  M. Wilde,et al.  Identifying the quantum correlations in light-harvesting complexes , 2009, 0912.5112.

[155]  M. Horodecki,et al.  Local versus nonlocal information in quantum-information theory: Formalism and phenomena , 2004, quant-ph/0410090.

[156]  Yong-Sheng Zhang,et al.  Experimental investigation of the non-Markovian dynamics of classical and quantum correlations , 2010, 1005.4510.

[157]  J. Maziero,et al.  Classicality witness for two-qubit states , 2010, 1012.3075.