Quantum perfect correlations

The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The transitivity of perfect correlations is proved to generally hold, and applied to a simple articulation for the failure of Hardy’s nonlocality proof for maximally entangled states. The notion of perfect correlations between observables and POVMs is used for defining the notion of a precise measurement of a given observable in a given state. A longstanding misconception on the correlation made by the measuring interaction is resolved in the light of the new theory of quantum perfect correlations.

[1]  P. Busch,et al.  The quantum theory of measurement , 1991 .

[2]  C. Ross.  Found , 1869, The Dental register.

[3]  T. Heinonen,et al.  Noise and disturbance in quantum measurement , 2004 .

[4]  Masanao Ozawa.  Operations, disturbance, and simultaneous measurability , 2001 .

[5]  Operator integrals and phase space observables , 1999 .

[6]  A. Raczyński,et al.  Symposium on the foundations of modern physics : edited by P. Lahti and P. Mittelstaedt, World Scientific Publishing Co. Pte. Ltd., Singapore 1985 , 1986 .

[7]  Masanao Ozawa.  Uncertainty relations for noise and disturbance in generalized quantum measurements , 2003 .

[8]  M. Ozawa.  Quantum measuring processes of continuous observables , 1984 .

[9]  K. Urbanik.  Joint probability distributions of observables in quantum mechanics , 1961 .

[11]  A. Holevo.  Statistical decision theory for quantum systems , 1973 .

[12]  E. Wigner.  On the quantum correction for thermodynamic equilibrium , 1932 .

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

[14]  M. Takesaki,et al.  Analyticity and the Unruh effect: a study of local modular flow , 2024, Journal of High Energy Physics.

[15]  E. Wigner.  The Problem of Measurement , 1963 .

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

[17]  J. E. Moyal.  Quantum mechanics as a statistical theory , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[18]  S. Berberian.  Notes on spectral theory , 1966 .

[19]  Vladimir B. Braginsky,et al.  Quantum Measurement , 1992 .

[20]  C. Helstrom.  Quantum detection and estimation theory , 1969 .

[21]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[22]  Quantum Perfect Correlations and Hardy’s Nonlocality Theorem , 1999, quant-ph/9908039.

[23]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[24]  L. Hardy,et al.  Nonlocality for two particles without inequalities for almost all entangled states. , 1993, Physical review letters.

[25]  John T. Lewis,et al.  An operational approach to quantum probability , 1970 .

[26]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[27]  Ericka Stricklin-Parker,et al.  Ann , 2005 .