Purification of Mixed State with Closed Timelike Curve is not Possible

Abstract

In ordinary quantum theory any mixed state can be purified in an enlarged Hilbert space by bringing an ancillary system. The purified state does not depend on the state of any extraneous system with which the mixed state is going to interact and on the physical interaction. Here, we prove that it is not possible to purify a mixed state that traverses a closed time like curve (CTC) and allowed to interact in a consistent way with a causality-respecting (CR) quantum system in the same manner. Thus, in general for arbitrary interactions between CR and CTC systems there is no universal 'Church of the larger Hilbert space' for mixed states with CTC. This shows that in quantum theory with CTCs there can exist 'proper' and 'improper' mixtures.

Latex2e, No Figs, 4 + pages, An error corrected, Results unchanged

References in corpus (5)

• Probabilistic theories with purification
• Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
• Information Flow of quantum states interacting with closed timelike curves
• Closed Timelike Curves Make Quantum and Classical Computing Equivalent
• Discontinuous quantum evolutions in the presence of closed timelike curves

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