Information-disturbance tradeoff in quantum measurement on the uniform ensemble

The author considers the tradeoff between information gained about a quantum state and disturbance caused by the measurement providing the information. For every measurement, he finds the way of making it which is least-disturbing, on average, when the initial quantum state is completely unknown.

[1]  Simon Litsyn,et al.  Quantum error detection I: Statement of the problem , 1999, IEEE Trans. Inf. Theory.

[2]  I. D. Ivonovic Geometrical description of quantal state determination , 1981 .

[3]  A. F. Foundations of Physics , 1936, Nature.

[4]  G. Illies,et al.  Communications in Mathematical Physics , 2004 .

[5]  Takuya Kon-no,et al.  Transactions of the American Mathematical Society , 1996 .

[6]  October I Physical Review Letters , 2022 .

[7]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[8]  E. Lieb Convex trace functions and the Wigner-Yanase-Dyson conjecture , 1973 .

[9]  P. Lugol Annalen der Physik , 1906 .

[10]  C. cohen-tannoudji,et al.  Quantum Mechanics: , 2020, Fundamentals of Physics II.

[11]  R. Werner OPTIMAL CLONING OF PURE STATES , 1998, quant-ph/9804001.

[12]  Eric M. Rains Polynomial invariants of quantum codes , 2000, IEEE Trans. Inf. Theory.

[13]  Günther Ludwig Foundations of quantum mechanics , 1983 .

[14]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[15]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[16]  T. Andô Concavity of certain maps on positive definite matrices and applications to Hadamard products , 1979 .

[17]  M. Sentís Quantum theory of open systems , 2002 .

[18]  A. Uhlmann The "transition probability" in the state space of a ∗-algebra , 1976 .

[19]  J. Seidel,et al.  BOUNDS FOR SYSTEMS OF LINES, AND JACOBI POLYNOMIALS , 1975 .

[20]  Harald Niederreiter,et al.  Introduction to finite fields and their applications: List of Symbols , 1986 .

[21]  Physical Review , 1965, Nature.

[22]  D. Bures An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite *-algebras , 1969 .

[23]  Charles H. Bennett,et al.  Quantum cryptography using any two nonorthogonal states. , 1992, Physical review letters.

[24]  Akademii︠a︡ medit︠s︡inskikh nauk Sssr Journal of physics , 1939 .

[25]  K R W Jones Quantum limits to information about states for finite dimensional Hilbert space , 1991 .

[26]  W. Wootters Random quantum states , 1990 .

[27]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[28]  Pérès,et al.  Quantum-state disturbance versus information gain: Uncertainty relations for quantum information. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[29]  A. Calderbank,et al.  Z4‐Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line‐Sets , 1997 .

[30]  R. Jozsa Fidelity for Mixed Quantum States , 1994 .

[31]  R. Jozsa,et al.  Lower bound for accessible information in quantum mechanics. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[32]  R. Werner,et al.  Optimal cloning of pure states, testing single clones , 1998, quant-ph/9807010.

[33]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[34]  Benjamin Schumacher Sending quantum entanglement through noisy channels , 1996 .

[35]  P. Morse Annals of Physics , 1957, Nature.

[36]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.