Related papers: Potent Value and Potent Operator with Pre- and Pos…

The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an…

It is argued that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems…

Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which…

Weak values are the fundamental values for observables in a pre- and post-selected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and post-selected system but the…

We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.

To describe the pre- and post-selected quantum ensembles, a complex quantity called the weak value of an operator is used. The weak value is highly controversial due to the fact that it is not bounded by the possible eigenvalues of the…

The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…

Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…

We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…

We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…

Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…

We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a…

Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify…

We show that the weak value of any observable in pre- and post-selected states can be expressed as the sum of the average of the observable in the pre-selected state and an anomalous part. We argue that at a fundamental level the anomalous…

In this paper we attempt to provide a physical representation of quantum superpositions. For this purpose we discuss the constraints of the quantum formalism to the notion of possibility and the necessity to consider a potential realm…

This paper presents some of the basic properties of conditioned observables in finite-dimensional quantum mechanics. We begin by defining the sequential product of quantum effects and use this to define the sequential product of two…

Various approaches of defining and determining work performed on a quantum system are compared. Any operational definition of work, however, must allow for two facts, first, that work characterizes a process rather than an instantaneous…

We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. Positive operator valued measures describe quantum observables and, similarly to quantum states, also quantum observables…

Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from…

We discuss a possibility to build a programmable quantum measurement device (a "quantum multimeter"). That is, a device that would be able to perform various desired generalized, positive operator value measure (POVM) measurements depending…