Can a quantum state over time resemble a quantum state at a single time?

Dominic Horsman, Christiaan Heunen, Matthew F. Pusey, Jonathan Barrett, Robert W. Spekkens

Research output: Contribution to journalArticlepeer-review

Abstract

Standard quantum theory represents a composite system at a given time by a joint state, but it does not prescribe a joint state for a composite of systems at different times. If a more even-handed treatment of space and time is possible, then such a joint state should be definable, and one might expect it to satisfy the following five conditions: that it is a Hermitian operator on the tensor product of the single-time Hilbert spaces; that it represents probabilistic mixing appropriately; that it has the appropriate classical limit; that it has the appropriate single-time marginals; that composing over multiple time-steps is associative. We show that no construction satisfies all these requirements. If an even-handed treatment of space and time is possible, therefore, one or more axioms must be dropped. In particular, if Hermiticity is dropped, then we show that the construction is fixed uniquely up to an ordering convention.
Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2205
DOIs
Publication statusPublished - 20 Sep 2017

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