Physical Purification of Quantum States

Abstract

We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a pure state in a higher-dimensional Hilbert space, the reduced density matrix of which is identical to the original state. We characterize all sets of mixed quantum states, for which perfect purification is possible. Surprisingly, some sets of two non-commuting states are among them. Furthermore, we investigate the possibility of performing an imperfect purification.

5 pages, 1 figure; published version

References in corpus (4)

• Noncommuting mixed states cannot be broadcast
• Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination
• A general scheme for ensemble purification
• Simultaneous decomposition of two states

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• Pure and mixed states
• $SU(\infty )$ Quantum Gravity and Cosmology
• Purifying and Reversible Physical Processes
• Geometric Constraints on Two-electron Reduced Density Matrices
• Thermal DMRG for highly frustrated quantum spin chains: a user perspective
• Quantum state of fields in $SU(\infty )$ Quantum Gravity ($SU(\infty )$-QGR)
• Finite-size scalings in measurement-induced dynamical phase transition