Conditional Density Operators and the Subjectivity of Quantum Operations
M. S. Leifer
备注：
10 Pages, Work presented at "Foundations of Probability and Physics-4", Vaxjo University, June 4-9 2006
发表信息：
G. Adenier, C. A. Fuchs and A. Yu. Khrennikov (eds.), Foundations of Probability and Physics - 4, AIP Conference Proceedings vol. 889, (AIP 2007), pp. 172-186
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is addressed. In particular, we ask this of the dynamical aspects of the formalism, such as Hamiltonians and unitary operators. Whilst some operations, such as the update maps corresponding to a complete projective measurement, must be subjective, the situation is not so clear in other cases. Here, it is argued that all trace preserving completely positive maps, including unitary operators, should be regarded as subjective, in the same sense as a classical conditional probability distribution. The argument is based on a reworking of the Choi-Jamiolkowski isomorphism in terms of "conditional" density operators and trace preserving completely positive maps, which mimics the relationship between conditional probabilities and stochastic maps in classical probability.
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Quantum conditional entropies from convex trace functionals
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）；Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电气与计算机工程系）
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