Symmetries of quantum evolutions
arXiv:2101.04962 · doi:10.1103/PhysRevResearch.3.033028
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.
arXiv comment11 + 11 pages, 1 figure, new results added, published version
References in corpus (62)
- Reference frames, superselection rules, and quantum information
- Fundamental limitations for quantum and nano thermodynamics
- Quantum correlations with no causal order
- Informational derivation of Quantum Theory
- Quantum computations without definite causal structure
- Theoretical framework for quantum networks
- Probabilistic theories with purification
- Structure of states which satisfy strong subadditivity of quantum entropy with equality
- The resource theory of informational nonequilibrium in thermodynamics
- Transforming quantum operations: quantum supermaps
- Tomography of Quantum Operations
- Reversing quantum dynamics with near-optimal quantum and classical fidelity
- Quantum conditional mutual information and approximate Markov chains
- Enhanced communication with the assistance of indefinite causal order
- Quantum from principles
- The completeness of quantum theory for predicting measurement outcomes
- Quasi-quantization: classical statistical theories with an epistemic restriction
- Introduction to the book "Quantum Theory: Informational Foundations and Foils"
- Memory effects in quantum channel discrimination
- Optimal quantum learning of a unitary transformation
- Quantum Operation Time Reversal
- Comparison of Quantum Channels by Superchannels
- Operational Resource Theory of Quantum Channels
- Is a time symmetric interpretation of quantum theory possible without retrocausality?
- Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
- Quantifying Operations with an Application to Coherence
- A resource theory of quantum memories and their faithful verification with minimal assumptions
- Resource Theory of Coherence - Beyond States
- On a Time Symmetric Formulation of Quantum Mechanics
- How to quantify a dynamical quantum resource
- A simple approach to approximate quantum error correction based on the transpose channel
- On the existence of physical transformations between sets of quantum states
- Application of the Resource Theory of Channels to Communication Scenarios
- Optimal cloning of unitary transformations
- Resource theory of asymmetric distinguishability for quantum channels
- Resource theories of communication
- Optimal quantum networks and one-shot entropies
- Quartic quantum theory: an extension of the standard quantum mechanics
- Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schrödinger Equations
- Dynamical Resource Theory of Quantum Coherence
- Theoretical framework for Higher-Order Quantum Theory
- Dynamical Entanglement
- Probabilistic exact universal quantum circuits for transforming unitary operations
- On Quantum Operations as Quantum States
- Operational formulation of time reversal in quantum theory
- Optimal quantum tomography for states, measurements, and transformations
- Coherence of quantum channels
- Dynamics of quantum causal structures
- Anti- (Conjugate) Linearity
- Microcanonical thermodynamics in general physical theories
- Decoding quantum information via the Petz recovery map
- Complex conjugation supermap of unitary quantum maps and its universal implementation protocol
- Time reversals of irreversible quantum maps
- Necessary and Sufficient Conditions on Measurements of Quantum Channels
- Quasi inversion of qubit channels
- Entanglement-breaking superchannels
- Units of rotational information
- Time-asymmetry of probabilities versus relativistic causal structure: an arrow of time
- Probabilistic storage and retrieval of qubit phase gates
- Subnormalized states and trace-nonincreasing maps
- Cloning of a quantum measurement
- Normal completely positive maps on the space of quantum operations
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- From time-reversal symmetry to quantum Bayes' rules
- The arrow of time in operational formulations of quantum theory
- Axioms for retrodiction: achieving time-reversal symmetry with a prior
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- Experimental superposition of time directions
- Experimental demonstration of input-output indefiniteness in a single quantum device
- Quantum communication through devices with indefinite input-output direction
- Energetic fluctuations in an open quantum process
- Quasi-inversion of quantum and classical channels in finite dimensions
- Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations
- Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
- Tsirelson bounds for quantum correlations with indefinite causal order
- Stochastic entropy production: Fluctuation relation and irreversibility mitigation in non-unital quantum dynamics
- Variations on the Choi-Jamiolkowski isomorphism
- Extracting the symmetries of nonequilibrium quantum many-body systems
- Entropic and operational characterizations of dynamic quantum resources
- Efficient measure of information backflow with a quasistochastic process