Probability Representation of Quantum Observables and Quantum States

被引：35
作者：
Chernega, Vladimir N. [1 ]
Man'ko, Olga V. [1 ,2 ]
Man'ko, Vladimir I. [1 ,3 ]
机构：
[1] Russian Acad Sci, Lebedev Phys Inst, Leninskii Prospect 53, Moscow 119991, Russia
[2] Bauman Moscow State Tech Univ, 2nd Baumanskaya Str 5, Moscow 105005, Russia
[3] State Univ, Moscow Inst Phys & Technol, Inst Skii Per 9, Dolgoprudnyi 141700, Moscow Region, Russia
来源：
JOURNAL OF RUSSIAN LASER RESEARCH | 2017年 / 38卷 / 04期
基金：
俄罗斯科学基金会;
关键词：
quantum suprematism; probability representation; quantum observables; qubit states; Heisenberg evolution equation; STAR PRODUCTS; SPIN; TOMOGRAPHY; TERMS;
D O I：
10.1007/s10946-017-9648-2
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation for quantum observables (Heisenberg equation) in the probability representation and give examples of the spin-1/2 (qubit) states and the spin observables. We present quantum channels for qubits in the probability representation.
引用
收藏
页码：324 / 333
页数：10
相关论文
共 44 条
[1]   Coherent states and the reconstruction of pure spin states [J].
Amiet, JP ;
Weigert, S .
JOURNAL OF OPTICS B-QUANTUM AND SEMICLASSICAL OPTICS, 1999, 1 (05) :L5-L8
[2]  
[Anonymous], NACH GES WISS GOTTIN
[3]  
[Anonymous], 2015, ADV CONCEPTS QUANTUM
[4]   Generalized tomographic maps [J].
Asorey, M. ;
Facchi, P. ;
Man'ko, V. I. ;
Marmo, G. ;
Pascazio, S. ;
Sudarshan, E. C. G. .
PHYSICAL REVIEW A, 2008, 77 (04)
[5]   Radon transform on the cylinder and tomography of a particle on the circle [J].
Asorey, M. ;
Facchi, P. ;
Man'ko, V. I. ;
Marmo, G. ;
Pascazio, S. ;
Sudarshan, E. G. C. .
PHYSICAL REVIEW A, 2007, 76 (01)
[6]   A TOMOGRAPHIC APPROACH TO WIGNER FUNCTION [J].
BERTRAND, J ;
BERTRAND, P .
FOUNDATIONS OF PHYSICS, 1987, 17 (04) :397-405
[7]   TRIANGLE GEOMETRY OF THE QUBIT STATE IN THE PROBABILITY REPRESENTATION EXPRESSED IN TERMS OF THE TRIADA OF MALEVICH'S SQUARES [J].
Chernega, Vladimir N. ;
Man'ko, Olga V. ;
Man'ko, Vladimir I. .
JOURNAL OF RUSSIAN LASER RESEARCH, 2017, 38 (02) :141-149
[8]   No signaling and strong subadditivity condition for tomographic q-entropy of single qudit states [J].
Chernega, Vladimir N. ;
Man'ko, Olga V. .
PHYSICA SCRIPTA, 2015, 90 (07)
[9]   Spin tomography [J].
D'Ariano, GM ;
Maccone, L ;
Paini, M .
JOURNAL OF OPTICS B-QUANTUM AND SEMICLASSICAL OPTICS, 2003, 5 (01) :77-84
[10]  
Dirac P. A. M., 1930, PRINCIPLES QUANTUM M
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