Quantum mechanics as an operationally time symmetric probabilistic theory


Oreshkov, O. (2013). Quantum mechanics as an operationally time symmetric probabilistic theory. Perimeter Institute. https://pirsa.org/13110057


Oreshkov, Ognyan. Quantum mechanics as an operationally time symmetric probabilistic theory. Perimeter Institute, Nov. 12, 2013, https://pirsa.org/13110057


          @misc{ pirsa_PIRSA:13110057,
            doi = {10.48660/13110057},
            url = {https://pirsa.org/13110057},
            author = {Oreshkov, Ognyan},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum mechanics as an operationally time symmetric probabilistic theory},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {nov},
            note = {PIRSA:13110057 see, \url{https://pirsa.org}}

Ognyan Oreshkov Université Libre de Bruxelles


The standard formulation of quantum mechanics is operationally asymmetric with respect to time reversal---in the language of compositions of tests, tests in the past can influence the outcomes of test in the future but not the other way around. The question of whether this represents a fundamental asymmetry or it is an artifact of the formulation is not a new one, but even though various arguments in favor of an inherent symmetry have been made, no complete time-symmetric formulation expressed in rigorous operational terms has been proposed. Here, we discuss such a possible formulation based on a generalization of the usual notion of test. We propose to regard as a test any set of events between an input and an output system which can be obtained by an autonomously defined laboratory procedure. This includes standard tests, as well as proper subsets of the complete set of outcomes of standard tests, whose realization may require post-selection in addition to pre-selection. In this approach, tests are not expected to be operations that are up to the choices of agents---the theory simply says what circuits of tests may occur and what the probabilities for their outcomes would be, given that they occur. By virtue of the definition of test, the probabilities for the outcomes of past tests can depend on tests that take place in the future. Such theories have been previously called non-causal, but here we revisit that notion of causality. Using the Choi-Jamiolkowski isomorphism, every test in that formulation, commonly regarded as inducing transformations from an input to an output system, becomes equivalent to a passive detection measurement applied jointly on two input systems---one from the past and one from the future. This is closely related to the two-state vector formalism, but it comes with a conceptual revision: every measurement is a joint measurement on two separate systems and not on one system described by states in the usual Hilbert space and its dual. We thus obtain a static picture of quantum mechanics in space-time or more general structures, in which every experiment is a local measurement on a global quantum state that generalizes the recently proposed quantum process matrix. The existence of two types of systems in the proposed formalism allows us to define causation in terms of correlations without invoking the idea of intervention, offering a possible answer to the problem of the meaning of causation. The framework is naturally compatible with closed time-like curves and other exotic causal structures.