History states of systems and operators

@article{Boette2018HistorySO,
  title={History states of systems and operators},
  author={A. Boette and Ra{\'u}l Rossignoli},
  journal={Physical Review A},
  year={2018}
}
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… 

Figures from this paper

Entanglement dynamics in a spin star system coupled weakly to a bosonic bath
TLDR
This work uses Born–Markov approximation to derive a master equation for the density operator of a spin star configuration and analyzes how the reservoir’s temperature and the value of system–environment coupling act on the behavior of entanglement.
Time Observables in a Timeless Universe
TLDR
It is shown here that Age, when introduced in the PaW context, can be interpreted as a proper Hermitian time operator conjugate to a "good" clock Hamiltonian, and it is demonstrated that Pegg's POVM states provide a consistent dynamical evolution of the system even if they are not orthogonal, and therefore partially un-distinguishables.
O ct 2 01 8 How to switch between relational quantum clocks
Every clock is a physical system and thereby ultimately quantum. A naturally arising question is thus how to describe time evolution relative to quantum clocks and, specifically, how the dynamics
Emergent dynamics from entangled mixed states
Entanglement is at the core of quantum physics, playing a central role in quantum phenomena involving composite systems. According to the timeless picture of quantum dynamics, entanglement may also
Parallel-in-time optical simulation of history states
We present an experimental optical implementation of a parallel-in-time discrete model of quantum evolution, based on the entanglement between the quantum system and a finite dimensional quantum
Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints
TLDR
Some properties of the measure D are investigated showing that, for increasing values of the interval's duration, the measure quickly reaches an asymptotic value given by the linear entropy of the energy distribution associated with the system’s (pure) quantum state.
Hermitian Time Operator in a Timeless Universe
Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without
History state formalism for scalar particles
We present a covariant quantum formalism for scalar particles based on an enlarged Hilbert space. The particular physical theory can be introduced through a timeless Wheeler DeWitt-like equation,
Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings
We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show
History state formalism for relativistic particles
A properly defined time operator, based on an enlarged Hilbert space H, is employed to embed the Dirac and Klein Gordon equations within a formalism where covariance is an explicit quantum symmetry
...
...

References

SHOWING 1-10 OF 78 REFERENCES
System-time entanglement in a discrete time model
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in
Relational time in anyonic systems
In a seminal paper [Phys. Rev. D 27, 2885 (1983)], Page and Wootters suggest that time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing
Time from quantum entanglement: an experimental illustration
In the last years several theoretical papers discussed if time can be an emergent property deriving from quantum correlations. Here, to provide an insight into how this phenomenon can occur, we
Feynman’s clock, a new variational principle, and parallel-in-time quantum dynamics
TLDR
A construction inspired by quantum computation that allows one to use virtually any model for a ground-state wavefunction to model quantum many-body dynamics and formulate it in a way that naturally leads to a parallel-in-time algorithm.
Channel kets, entangled states, and the location of quantum information (16 pages)
TLDR
It is proposed that both channel and entanglement problems be classified in terms of pure statesmore,functioning as pre-probabilities on systems of p{>=}2 parts, with mixed bipartiteEntanglement and simple noisy channels belonging to the category p=3, a five-qubit code to the categories p=6, etc., then by the dimensions of the Hilbert spaces of the component parts, along with other criteria yet to be determined.
Entanglement of quantum clocks through gravity
TLDR
It is shown that the general relativistic mass–energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background.
Unitary quantum gates, perfect entanglers, and unistochastic maps
Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U equal to the Shannon
Investigating the emergence of time in stationary states with trapped ions
Even though quantum systems in energy eigenstates do not evolve in time, they can exhibit correlations between internal degrees of freedom in such a way that one of the internal degrees of freedom
Standard forms of noisy quantum operations via depolarization
We consider completely positive maps that describe noisy, multiparticle unitary operations. We show that by random single-particle operations the completely positive maps can be depolarized to a
Effective approach to the problem of time: general features and examples
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type.
...
...