#### Document Type

Conference Proceeding

#### Publication Date

2006

#### Abstract

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-Jamiołkowski 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.

#### Recommended Citation

Leifer, M.S., 2006. Conditional Density Operators and the Subjectivity of Quantum Operations. *AIP Conference Proceedings*, 889, 172—186. doi:10.1063/1.2713456

#### Copyright

American Institute of Physics

## Comments

This is an author-prepared, prepublication version of a paper that was presented at Foundations of Probability and Physics 4 in 2006 and was later published in

AIP Conference Proceedings, vol. 889, edited by G. Adenier, C. A. Fuchs and A. Yu. Khrennikov, pp. 172—186 (2007). DOI: 10.1063/1.2713456