Operational quantum theory without predefined time

Operational quantum theory without predefined time

Seminar author:Ognyan Oreshkov

Event date and time:11/12/2014 02:10:pm

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The current operational formulation of quantum theory is
based on the concept of operation with an input and an output system,
which assumes a prior notion of time and is asymmetric under time
reversal. But in certain contexts, such as those involving gravity,
time is expected to be dynamical and not predefined. In this talk, I
will describe a proposal for an operational formulation of quantum
theory without any predefined notion of time. After critically
examining the implicit assumptions underlying the standard concept of
operation, I will propose a generalization of that concept based on an
epistemic approach: an operation is a description of knowledge about
the events in a given region, which can be updated conditionally on
information obtained from that region. First assuming a background
time, I will show how this approach leads us to an operationally
time-symmetric quantum theory. I will make precise the notion of time
reversal symmetry and clarify several misconceptions. I will present a
generalization of Wigner’s theorem which puts time-reversal symmetry
on operational grounds, and will show that the developed operationally
time-symmetric theory allows for more general symmetry transformations
than those assumed before. I will explain how the time-reversal
asymmetry we observe can be understood as due to boundary conditions
and will establish a link between that asymmetry and the fact that we
remember the past but not the future. I will then introduce a
mathematical formalism that allows us to completely drop the
assumption of predefined time. In the resultant formulation of quantum
theory, operations are associated with regions with boundary systems
and can be connected in networks with no directionality assumed for
the connections, generalizing the standard circuit picture. The events
associated with an operation are described by positive semidefinite
operators on the Hilbert spaces of the boundary systems, while the
connections between regions are described by entangled states that
encode a nontrivial physical symmetry. A simple rule provides the
joint probabilities for the events in a network of operations. I will
discuss how it may be possible to understand the emergence of a causal
structure in space-time from properties of the operators on the
boundaries of compact space-time regions. The framework allows for
indefinite causal order, timelike loops, and other acausal structures.

Based on: http://arxiv.org/abs/1406.3829