Quantumness of correlations revealed in local measurements exceeds entanglement

We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement monotone $E$, this operational correspondence provides a different measure $Q_E$ of quantum correlations. Examples of such measures are the relative entropy of quantumness, the quantum deficit, and the negativity of quantumness. In general, we prove that any so defined quantum correlation measure is always greater than (or equal to) the corresponding entanglement between the subsystems, $Q_E \ge E$, for arbitrary states of composite quantum systems. We analyze qualitatively and quantitatively the flow of correlations in iterated measurements, showing that general quantum correlations and entanglement can never decrease along von Neumann chains, and that genuine multipartite entanglement in the initial state of the observed system always gives rise to genuine multipartite entanglement among all subsystems and all measurement apparatuses at any level in the chain. Our results provide a comprehensive framework to understand and quantify general quantum correlations in multipartite states.

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

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

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

[4]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

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

[6]  W. Zurek.  Decoherence, einselection, and the quantum origins of the classical , 2001, quant-ph/0105127.

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

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

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

[10]  Sergei Bravyi.  Entanglement entropy of multipartite pure states , 2003 .

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

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

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

[14]  W. Zurek.  The Environment, Decoherence and the Transition from Quantum to Classical , 1991 .

[15]  S. Wehner,et al.  The Uncertainty Principle Determines the Nonlocality of Quantum Mechanics , 2010, Science.

[16]  M. Horodecki,et al.  Locking classical correlations in quantum States. , 2003, Physical review letters.

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

[18]  J. Neumann.  Mathematical Foundations of Quantum Mechanics , 1955 .

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

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

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

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

[23]  Vlatko Vedral,et al.  Quantum Correlations in Mixed-State Metrology , 2010, 1003.1174.

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

[25]  Carlton M. Caves,et al.  ENTROPIC MEASURES OF NON-CLASSICAL CORRELATIONS , 2011, 1105.4920.

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

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

[28]  Z. Merali.  Quantum computing: The power of discord , 2011, Nature.

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

[30]  Martin B. Plenio,et al.  An introduction to entanglement measures , 2005, Quantum Inf. Comput..

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

[32]  R. Zambrini,et al.  Genuine quantum and classical correlations in multipartite systems. , 2011, Physical review letters.

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

[34]  V. Vedral,et al.  Classical, quantum and total correlations , 2001, quant-ph/0105028.

[35]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

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

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

[38]  H. Reck.  Der Ausbruchscyklus des Merapi in den Jahren 1933/34 , 1935, Naturwissenschaften.

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

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

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

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

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

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

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

[46]  Hermann Kampermann,et al.  Behavior of quantum correlations under local noise. , 2011, Physical review letters.

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

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

[49]  M. Horodecki,et al.  The entanglement of purification , 2002, quant-ph/0202044.

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

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

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