Related papers: Positive operator-valued measures in quantum decis…
From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive…
We develop a new formalism for constructing probabilities associated to the causal ordering of events in quantum theory, where by an event we mean the emergence of a measurement record on a detector. We start with constructing probabilities…
Entanglement is a key resource to demonstrate quantum advantage over classical strategies. Entanglement in quantum states is one of the most well-explored areas in quantum physics. However, a rigorous approach to understanding and detecting…
From an operational point of view, we propose several new entanglement detection criteria using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter-intuitively, the criteria…
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of…
Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…
Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize…
Motivated by the increasing ability of experimentalists to perform detector tomography, we consider how to incorporate the imperfections and restrictions of available measurements directly into the quantification of entanglement. Exploiting…
The minimum error probability for distinguishing between two quantum states is bounded by the Helstrom limit, derived under the assumption that measurement strategies are restricted to positive operator-valued measurements. We explore…
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
Classically the causal order of two timelike separated events A and B is fixed -- either A before B or B before A. This is no longer true in quantum theory, where it is possible to encounter superpositions of causal orders. The quantum…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to…
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…