2021/01/31 by Giulio Chiribella, Erik Aurell, Karol Życzkowski
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Open quantum system #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum dissipation #Quantum dynamics #Quantum operation #Quantum probability #Quantum process #Quantum state #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevresearch.3.033028
published as Phys. Rev. Research 3, 033028 (2021) · 11 + 11 pages, 1 figure, new results added, published version
openalex created_date 2021/06/07 · arxiv created 2021/06/08 · openalex publication_date 2021/07/06 · arxiv updated 2021/07/14 · openalex updated_date 2026/08/05
A cornerstone of quantum mechanics is the characterization 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 with the dynamics of closed systems and the stochastic evolutions associated with 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.