Related papers: Quantum Instruments and Conditioned Observables
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…
Quantum technology has been rapidly growing due to its potential revolutionary applications. In particular, superconducting qubits provide a strong light-matter interaction as required for quantum computation and in principle can be scaled…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
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…
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead…
In Quantum Physics there are circumstances where the direct measurement of particular observables encounters diffculties; in some of these cases, however, its value can be evaluated, i.e. it can be inferred by measuring another observable…
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…
We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104 240401 (2010)]. The theory of contextual values extends the well-established theory…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
Our basic concept is the set $\mathcal{E}(H)$ of effects on a finite dimensional complex Hilbert space $H$. If $a,b\in\mathcal{E}(H)$, we define the sequential product $a[\mathcal{I}]b$ of $a$ then $b$. The sequential product depends on the…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
A time-dependent product is introduced between the observables of a dissipative quantum system, that accounts for the effects of dissipation on observables and commutators. In the $t \to \infty$ limit this yields a contracted algebra. The…
The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of…