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Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…
We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on…
A projective quantum logic in terms of relative states is developed, emphasizing the importance of information transfer between a system under study and its environment. The need for accounting for the historical evolution of system is…
Recently, there have been several suggestions that weak Kerr nonlinearity can be used for generation of macroscopic superpositions and entanglement and for linear optics quantum computation. However, it is not immediately clear that this…
The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…
The concept of decoherence is defined, and discussed in a historical context. This is illustrated by some of its essential consequences which may be relevant for the interpretation of quantum theory. Various aspects of the formalism are…
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…
Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on…
Probabilities in quantum theory are traditionally given by Born's rule as the expectation values of projection operators. Here it is shown that Born's rule is insufficient in universes so large that they contain identical multiple copies of…
Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular…
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the…
Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Understanding quantum theory has been a subject of debate from its birth. Many different formulations and interpretations have been proposed. Here we examine a recent novel formulation, namely the coevents formulation. It is a histories…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
In this paper, we analyze the quantum counting under the decoherence, which can find the number of solutions satisfying a given oracle. We investigate probability distributions related to the first order term of the error rate on the…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…