Intrinsic Quantum Computation

We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information between a quantum process's past and its future. The second, the quantum transient information, determines the difficulty with which an observer comes to know the internal state of a quantum process through measurements. We contrast these with von Neumann entropy and quantum entropy rate and provide a closed-form expression for the latter for the class of deterministic quantum processes.

[1]  Henri Poincaré,et al.  méthodes nouvelles de la mécanique céleste , 1892 .

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

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

[4]  J. Crutchfield,et al.  Statistical complexity of simple one-dimensional spin systems , 1997, cond-mat/9702191.

[5]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[6]  J. Crutchfield,et al.  Regularities unseen, randomness observed: levels of entropy convergence. , 2001, Chaos.

[7]  L. Ballentine,et al.  Quantum Theory: Concepts and Methods , 1994 .

[8]  A. Messiah.  Quantum Mechanics, Volume II , 1981 .

[9]  Debbie W. Leung,et al.  Realization of quantum process tomography in NMR , 2000, quant-ph/0012032.

[10]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[11]  W. Zurek,et al.  Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information , 2005, quant-ph/0505031.

[12]  Mark Fannes,et al.  Quantum Dynamical Systems , 2001 .

[13]  R. Feynman.  Simulating physics with computers , 1999 .

[14]  A. Wehrl.  General properties of entropy , 1978 .

[15]  S. Massar,et al.  Quantum information processing and communication , 2005 .

[16]  Linda E Reichl,et al.  The Transition to Chaos: Conservative Classical Systems and Quantum Manifestations , 2004 .

[17]  J.Dziarmaga,et al.  Unconditional Pointer States from Conditional Master Equations , 2000 .

[18]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[19]  Wojciech H. Zurek,et al.  Predictability sieve, pointer states, and the classicality of quantum trajectories (10 pages) , 2005 .

[20]  Hideo Mabuchi,et al.  Real-Time Quantum Feedback Control of Atomic Spin-Squeezing , 2004, Science.

[21]  Kurt Jacobs,et al.  Emergence of chaos in quantum systems far from the classical limit. , 2006, Physical review letters.

[22]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

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

[24]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[25]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[26]  Isaac L. Chuang,et al.  Prescription for experimental determination of the dynamics of a quantum black box , 1997 .

[27]  C. Beck,et al.  Symbolic dynamics of successive quantum-mechanical measurements. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[28]  P. Zoller,et al.  Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate , 1996, quant-ph/9611013.

[29]  Jorge V. José,et al.  Chaos in classical and quantum mechanics , 1990 .