Symmetries of quantum evolutions
- URL: http://arxiv.org/abs/2101.04962v5
- Date: Tue, 8 Jun 2021 06:45:02 GMT
- Title: Symmetries of quantum evolutions
- Authors: Giulio Chiribella, Erik Aurell, and Karol \.Zyczkowski
- Abstract summary: Wigner's theorem establishes that every symmetry of quantum state space must be either a unitary transformation, or an antiunitary transformation.
We show that it is impossible to extend the time reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions.
Our no-go theorem implies that any time symmetric formulation of quantum theory must either restrict the set of the allowed evolutions, or modify the operational interpretation of quantum states and processes.
- Score: 0.5735035463793007
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A cornerstone of quantum mechanics is the characterisation of symmetries
provided by Wigner's theorem. Wigner's theorem establishes that every symmetry
of the quantum state space must be either a unitary transformation, or an
antiunitary transformation. Here we extend Wigner's theorem from quantum states
to quantum evolutions, including both the deterministic evolution associated to
the dynamics of closed systems, and the stochastic evolutions associated to the
outcomes of quantum measurements. We prove that every symmetry of the space of
quantum evolutions can be decomposed into two state space symmetries that are
either both unitary or both antiunitary. Building on this result, we show that
it is impossible to extend the time reversal symmetry of unitary quantum
dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem
implies that any time symmetric formulation of quantum theory must either
restrict the set of the allowed evolutions, or modify the operational
interpretation of quantum states and processes. Here we propose a time
symmetric formulation of quantum theory where the allowed quantum evolutions
are restricted to a suitable set, which includes both unitary evolution and
projective measurements, but excludes the deterministic preparation of pure
states. The standard operational formulation of quantum theory can be retrieved
from this time symmetric version by introducing an operation of conditioning on
the outcomes of past experiments.
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