Related papers: Weak Values as Context Dependent Values of Observa…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
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…
We address two major conceptual developments introduced by Aharonov and collaborators through a \textit{quantum phase space} approach: the concept of \textit{modular variables} devised to explain the phenomena of quantum dynamical…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
An operational approach to quantum state reduction, the state change of the measured system caused by a measurement of an observable conditional upon the outcome of measurement, is founded without assuming the projection postulate in any…
The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it…
The noncontextuality condition states that a value of any observable is independent of which other compatible observable is measured jointly with it. Klyachko, Can, Binicio{\u{g}}lu, and Shumovsky have introduced an inequality which holds…
A simple proof is given that the probabilities of observations in a large universe are not given directly by Born's rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative…
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the…
In an earlier publication we had given an exhaustive analysis of the criteria for weak value measurements of pure states to be optimal in the sense considered by Wootters and Fields. We had proved, for arbitrary spin cases, that the…
Probabilities for observations in cosmology are conditioned both on the universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional…
In the Aharonov-Albert-Vaidman (AAV) weak measurement, it is assumed that the measuring device or the pointer is in a quantum mechanical pure state. In reality, however, it is often not the case. In this paper, we generalize the AAV weak…
Weak values of quantum observables are a powerful tool for investigating quantum phenomena. Some methods for measuring weak values in the laboratory require weak interactions and postselection, while others are deterministic, but require…
We show that the quadratic measure need not be postulated, but follows from the compatibility of two structural features of physical processes: linear reversible evolution prior to the formation of persistent records, and multiplicative…
Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100? In 1988 Aharonov, Albert and Vaidman argued that upon pre- and postselection of particular spin states, weakening the coupling of a standard…
Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its…
We extend the idea of weak measurements to the general case, provide a complete treatment and obtain results for both the regime when the pre-selected and post-selected states (PPS) are almost orthogonal and the regime when they are exactly…
The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the…