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It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our…
We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
It is shown how consistent histories quantum cosmology can be realised through Isham's Histories Projection Operator consistent histories scheme. This is done by using an affine algebra instead of a canonical one and also by using cocycle…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and…
The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed…
A new solution is proposed to the long-standing problem of describing the quantum phase of a harmonic oscillator. In terms of an'exponential phase operator', defined by a new 'polar decomposition' of the quantized amplitude of the…
Non-relativistic quantum theory of non-interacting particles in the spacetime containing a region with closed time-like curves (time-machine spacetime) is considered with the help of the path-integral technique. It is argued that, in…
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows all real eigen-energy spectrum.…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to…
The projector onto single quantum map eigenstates is written only in terms of powers of the evolution operator, up to half the Heisenberg time, and its traces. These powers are semiclassically approximated, by a complex generating function,…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
We establish the equivalence between the quantum evolution of spatially homogeneous oscillations of a scalar field and that of an analogous classical system with certain random initial condition. We argue that this observation can be used…
The decoherent histories approach is a natural medium in which to address problems in quantum theory which involve time in a non-trivial way. This article reviews the various attempts and difficulties involved in using the decoherent…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…