Related papers: Weak value analogue in classical stochastic proces…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
The weak value, introduced by Aharonov et al. to extend the conventional scope of physical observables in quantum mechanics, is an intriguing concept which sheds new light on quantum foundations and is also useful for precision measurement,…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
A classical system, which is analogous to the quantum one with a backflow of probability, is proposed. The system consists of a chain of masses interconnected by springs, as well attached by other springs to fixed supports. Thanks to the…
The readings of a highly inaccurate "weak" quantum meter, employed to determine the value of a dichotomous variable $S$ without destroying the interference between the alternatives,may take arbitrary values. We show that the expected values…
We examine the logical structure of the emergence of classical stochasticity for a quantum system governed by a Pauli-type master equation. It is well-known that while such equations describe the evolution of probabilities, they do not…
The question of what is genuinely quantum about weak values is only ever going to elicit strongly subjective opinions---it is not a scientific question. Good questions, when comparing theories, are operational---they deal with the…
How much information do we need about a process' past to faithfully simulate its future? The statistical complexity is a prominent quantifier of structure for stochastic processes. Quantum machines, however, can simulate classical…
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…
We present a complex probability measure relevant for double (pairs of) states in quantum mechanics, as an extension of the standard probability measure for single states that underlies Born's statistical rule. When the double states are…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…
Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a…
This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based…
A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators (such as values less than zero) always…
We consider a case where a weak value is introduced as a physical quantity rather than an average of weak measurements. The case we treat is a time evolution of a particle by 1+1 dimensional Dirac equation. Particularly in a spontaneous…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
The time derivative of a physical property often gives rise to another meaningful property. Since weak values provide empirical insights that cannot be derived from expectation values, this paper explores what physical properties can be…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…