Weak values of a quantum observable and the cross-Wigner distribution

被引:11
作者
de Gosson, Maurice A. [1 ]
de Gosson, Serge M. [2 ]
机构
[1] Univ Vienna, Fac Math, NuHAG, A-1090 Vienna, Austria
[2] Swedish Social Insurance Agcy, Dept Anal & Forecasts, S-10351 Stockholm, Sweden
关键词
Weak values; Weak measurements; Wigner distribution; Interference; PHASE-SPACE; ELEMENTS; REALITY;
D O I
10.1016/j.physleta.2011.11.007
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor here is the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:293 / 296
页数:4
相关论文
共 31 条
[1]   TIME SYMMETRY IN QUANTUM PROCESS OF MEASUREMENT [J].
AHARONOV, Y ;
BERGMANN, PG ;
LEBOWITZ, JL .
PHYSICAL REVIEW B, 1964, 134 (6B) :1410-&
[2]   Quantum averages of weak values [J].
Aharonov, Y ;
Botero, A .
PHYSICAL REVIEW A, 2005, 72 (05)
[3]   HOW THE RESULT OF A MEASUREMENT OF A COMPONENT OF THE SPIN OF A SPIN-1/2 PARTICLE CAN TURN OUT TO BE 100 [J].
AHARONOV, Y ;
ALBERT, DZ ;
VAIDMAN, L .
PHYSICAL REVIEW LETTERS, 1988, 60 (14) :1351-1354
[4]   PROPERTIES OF A QUANTUM SYSTEM DURING THE TIME INTERVAL BETWEEN 2 MEASUREMENTS [J].
AHARONOV, Y ;
VAIDMAN, L .
PHYSICAL REVIEW A, 1990, 41 (01) :11-20
[5]   A time-symmetric formulation of quantum mechanics [J].
Aharonov, Yakir ;
Popescu, Sandu ;
Tollaksen, Jeff .
PHYSICS TODAY, 2010, 63 (11) :27-32
[6]  
Aharonov Y, 2008, LECT NOTES PHYS, V734, P399, DOI 10.1007/978-3-540-73473-4_13
[7]  
[Anonymous], [No title captured]
[8]   RADAR AMBIGUITY FUNCTIONS AND GROUP-THEORY [J].
AUSLANDER, L ;
TOLIMIERI, R .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1985, 16 (03) :577-601
[9]   Complex density probability in non-Hermitian quantum mechanics: Interpretation and a formula for resonant tunneling probability amplitude [J].
Barkay, H ;
Moiseyev, N .
PHYSICAL REVIEW A, 2001, 64 (04) :4
[10]   Typical weak and superweak values [J].
Berry, M. V. ;
Shukla, P. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (35)