Related papers: Insufficiency of the Quantum State for Deducing Ob…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
In this article, we revisit the century-old question of the minimal set of observables needed to identify a quantum state: here, we replace the natural coincidences in their spectra by effective ones, induced by an imperfect measurement. We…
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,…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d^2 independent elements, where d is the number of possible outcomes for a precise measurement of an…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical…
Measurement is an important scientific activity. In most of science, including classical physics, is may be understood as a way of finding out about the physical world and representing the results numerically. No-go theorems show that…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
The concept of {\em complexity} (as a quantity) has been plagued by numerous contradictory and confusing definitions. By explicitly recognising a role for the observer of a system, an observer that attaches meaning to data about the system,…
We analyze the restrictions on the distinguishability of quantum states imposed by special relativity. An explicit expression relating the error probability for distinguishing between two orthogonal single-photon states with the time $T$…
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum…
Essential elements of quantum theory are derived from an epistemic point of view, i.e., the viewpoint that thetheory has to do with what can be said about nature. This gives a relationship to statistical reasoning and to other areas of…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…