Related papers: Two questions on quantum statistics
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
The purpose of quantum tomography is to determine an unknown quantum state from measurement outcome statistics. There are two obvious ways to generalize this setting. First, our task need not be the determination of any possible input state…
We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help…
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,…
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…
We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the…
The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…
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…
Counting outcomes is the obvious algorithm for generating probabilities in quantum mechanics without state-vector reduction (i.e. many-worlds). This procedure has usually been rejected because for purely linear dynamics it gives results in…
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $\psi$-ontic quantum theories, reality is directly represented by the wavefunction. We show that…
In the modern quantum mechanics of cosmology observers are physical systems within the universe. They have no preferred role in the formulation of the theory nor in its predictions of third person probabilities of what occurs. However,…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. We propose a novel scheme where identical copies of a quantum state are measured jointly so that all Pauli…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
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…
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…
Quantum mechanics relates probability of an observable event to the absolute square of the corresponding probability amplitude. It may, therefore, seem that the information about the amplitudes' phases must be irretrievably lost in the…