Related papers: Complex Probability Measure and Aharonov's Weak Va…
The Born rule for probabilities of measurement results is deduced from the set of five assumptions. The assumptions state that: (a) the state vector fully determines the probabilities of all measurement results; (b) between measurements,…
In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
We propose a new class of probabilistic reversing operations on the state of a system that was disturbed by a weak measurement. It can approximately recover the original state from the disturbed state especially with an additional…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
Recently, the notions of Weak Measurement (WM), Weak Value (WV) and Two-State-Vector Formalism (TSVF), firstly introduced by Aharonov and collaborators, have extended the theoretical frame of standard quantum mechanics, thus providing a…
Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…
Weak measurements are a new tool for characterizing post-selected quantum systems during their evolution. Weak measurement was originally formulated in terms of von Neumann interactions which are practically available for only the simplest…
Recently, weak value $\rm A_w$ derived in the pre- and post-selected weak measurement has been shown to be powerful in measuring minute physical effects. In principle, the decrease in the post-selection probability will increase the…
In this, partly pedagogical review, I attempt to give a self-contained overview of the basis of (non-relativistic) QM measurement theory expressed in density matrix formalism. The focus is on applications to the theory of weak measurement,…
Weak measurements may result in extra quantity of quantumness of correlations compared with standard projective measurement on a bipartite quantum state. We show that the quantumness of correlations by weak measurements can be consumed for…
Two basic properties of the set of all probability measures on the set of quantum states and their corollaries are considered. Several applications of these properties to analysis of functional constructions widely used in quantum…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
Quantum mechanics has withstood every experimental test thus far. However, it relies on ad-hoc postulates which require experimental verification. Over the past decade there has been a great deal of research testing these postulates, with…
A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
The indeterminism of quantum mechanics generally permits the independent specification of both an initial and a final condition on the state. Quantum pre-and-post-selection of states opens up a new, experimentally testable, sector of…