History states of systems and operators
arXiv:1806.00956 · doi:10.1103/PhysRevA.98.032108
Abstract
We discuss some fundamental properties of discrete system-time history states. Such states arise for a quantum reference clock of finite dimension and lead to a unitary evolution of system states when satisfying a static discrete Wheeler-DeWitt-type equation. We consider the general case where system-clock pairs can interact, analyzing first their different representations and showing there is always a special clock basis for which the evolution for a given initial state can be described by a constant Hamiltonian . It is also shown, however, that when the evolution operators form a complete orthogonal set, the history state is maximally entangled for any initial state, as opposed to the case of a constant , and can be generated with a simple two-clock setting. We then examine the quadratic system-time entanglement entropy, providing an analytic evaluation and showing it satisfies strict upper and lower bounds determined by the energy spread and the geodesic evolution connecting the initial and final states. We finally show that the unitary operator that generates the history state can itself be considered as an operator history state, whose quadratic entanglement entropy determines its entangling power. Simple measurements on the clock enable to efficiently determine overlaps between system states and also evolution operators at any two times.
arXiv comment10 pages, 4 figures, final version
References in corpus (29)
- Symmetric Informationally Complete Quantum Measurements
- Floquet Time Crystals
- On the Power of One Bit of Quantum Information
- On the Entangling Power of Quantum Evolutions
- Quantum interferometric visibility as a witness of general relativistic proper time
- Operator space entanglement entropy in transverse Ising chain
- Quantum dynamics as a physical resource
- Quantum Time
- Conditional probabilities with Dirac observables and the problem of time in quantum gravity
- Time from quantum entanglement: an experimental illustration
- Autonomous quantum clocks: does thermodynamics limit our ability to measure time?
- Effective approach to the problem of time: general features and examples
- Standard forms of noisy quantum operations via depolarization
- Entanglement of quantum clocks through gravity
- Effective relational dynamics of a nonintegrable cosmological model
- Operator fidelity susceptibility: an indicator of quantum criticality
- Heisenberg-Weyl Observables: Bloch vectors in phase space
- Unitary quantum gates, perfect entanglers and unistochastic maps
- Violation of majorization relations in entangled states and its detection by means of generalized entropic forms
- System-time entanglement in a discrete time model
- Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics
- Quantum Time: experimental multi-time correlations
- Geometric characteristics of quantum evolution: curvature and torsion
- Channel kets, entangled states, and the location of quantum information
- Space-time symmetric extension of non-relativistic quantum mechanics
- Clock Quantum Monte Carlo: an imaginary-time method for real-time quantum dynamics
- Relational time in anyonic systems
- Investigating the origin of time with trapped ions
- Entangling Power in the Deterministic Quantum Computation with One Qubit
Cited by in corpus (19)
- The Trinity of Relational Quantum Dynamics
- Equivalence of approaches to relational quantum dynamics in relativistic settings
- How to switch between relational quantum clocks
- History state formalism for scalar particles
- Time Observables in a Timeless Universe
- Spacetime Quantum Actions
- Quantifying quantum reference frames in composed systems: local, global and mutual asymmetries
- A model of quantum spacetime
- Peaceful coexistence of thermal equilibrium and the emergence of time
- Spacetime quantum and classical mechanics with dynamical foliation
- Parallel-in-time optical simulation of history states
- Path Integrals from Spacetime Quantum Actions
- Space-time-symmetric extension of quantum mechanics: Interpretation and arrival-time predictions
- Emergent dynamics from entangled mixed states
- Parallel-in-time quantum simulation via Page and Wootters quantum time
- History states of one-dimensional quantum walks
- Time dilation of quantum clocks in a relativistic gravitational potential
- Relational Dynamics with Periodic Clocks
- Representations of two-qubit and ququart states via discrete Wigner functions