Related papers: At what time does a quantum experiment have a resu…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
Quantum measurement not only can destroy coherence but also can create it. Here, we estimate the maximum amount of coherence, one can create under a complete non-selective measurement process. For our analysis, we consider projective as…
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…
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from…
The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The…
We suggest and describe how to analyze new types of experiments that would test a proposed model of the quantum measurement process. That model produces the Born Rule as a corollary, and so agrees with conventional quantum predictions. The…
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a…
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert…
The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $\psi$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of…
We identify an operational principle that singles out Projection-Valued Measures (PVMs) among general Positive Operator-Valued Measures (POVMs), bridging the modern quantum measurement theory and the traditional formulation based on…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
In this report, we present a framework for implementing an arbitrary $n$-outcome generalized quantum measurement (POVM) on an $m$-qubit register as a sequence of two-outcome measurements requiring only single ancillary qubit. Our procedure…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
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…
In Everett's many worlds interpretation, quantum measurements are considered to be decoherence events. If so, then inexact decoherence may allow large worlds to mangle the memory of observers in small worlds, creating a cutoff in observable…
Zurek's derivation of Born's rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to measurement of a quantum observable. Contrariwise, textbook formulations…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…
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…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
I argue that the rules of unitary quantum mechanics imply that observers who will themselves be subject to measurements in a linear combination of macroscopic states (``cat" measurements) cannot make reliable predictions on the results of…