Related papers: Quantum recurrence of a subspace and operator-valu…
We consider quantum dynamical systems specified by a unitary operator U and an initial state vector \phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We…
In this work we study the recurrence problem for quantum Markov chains, which are quantum versions of classical Markov chains introduced by S. Gudder and described in terms of completely positive maps. A notion of monitored recurrence for…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…
We introduce a novel time-energy uncertainty relation within the context of restarts in monitored quantum dynamics. Initially, we investigate the concept of ``first hitting time'' in quantum systems using an IBM quantum computer and a…
This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting…
Measurements on a quantum particle unavoidably affect its state, since the otherwise unitary evolution of the system is interrupted by a non-unitary projection operation. In order to probe measurement-induced effects in the state dynamics…
Recurrence time quantifies the duration required for a physical system to return to its initial state, playing a pivotal role in understanding the predictability of complex systems. In quantum systems with subspace measurements, recurrence…
The recurrence time is the time a process first returns to its initial state. Using quantum walks on a graph, the recurrence time is defined through stroboscopic monitoring of the arrival of the particle to a node of the system. When the…
Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum…
Quantum dynamics that explore an unexpectedly small fraction of Hilbert space is inherently interesting. Integrable systems, quantum scars, MBL, hidden tensor structures, and systems with gauge symmetries are examples. Beyond dimension and…
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases.…
Recent work on recurrence in quantum walks has provided a representation of Schur functions in terms of unitary operators. We propose a generalization of Schur functions by extending this operator representation to arbitrary operators on…
This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical…
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…
We develop a unified spectral-semigroup framework that connects real-time and imaginary-time quantum dynamics through analytic continuation. Within this formulation, evolution is expressed as an exponential reweighting of spectral…
The quantum Schur transform is a fundamental building block that maps the computational basis to a coupled basis consisting of irreducible representations of the unitary and symmetric groups. Equivalently, it may be regarded as a change of…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
This work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
Schwinger's algebra of selective measurements has a natural interpretation in the formalism of groupoids. Its kinematical foundations, as well as the structure of the algebra of observables of the theory, was presented in two previous…