Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Quantum Physics
Quantum Dynamics As An Analog Of Conditional Probability, Matthew S. Leifer
Quantum Dynamics As An Analog Of Conditional Probability, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
Quantum theory can be regarded as a noncommutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the well-known isomorphism between completely positive maps and bipartite density operators is derived, which makes this connection much more explicit. This isomorphism is given an operational interpretation in terms of statistical correlations between ensemble preparation procedures and outcomes of measurements. Finally, the isomorphism is applied to elucidate the connection between no-cloning and no-broadcasting theorems and the monogamy of entanglement, and a simplified proof of the no-broadcasting …
Conditional Density Operators And The Subjectivity Of Quantum Operations, Matthew S. Leifer
Conditional Density Operators And The Subjectivity Of Quantum Operations, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
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 …