Related papers: Positive operator-valued measures in quantum decis…
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,…
Entanglement witnesses provide tools to detect entanglement in experimental situations without the need of having full tomographic knowledge about the state. If one estimates in an experiment an expectation value smaller than zero, one can…
In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…
We demonstrate that temporal observables, which are sensitive to a system's history (as opposed to its state), implicate entangled histories. We exemplify protocols for measuring such observables, and algorithms for predicting the…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic.…
A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is…
We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to…
We consider a family of vector and operator norms defined by the Schmidt decomposition theorem for quantum states. We use these norms to tackle two fundamental problems in quantum information theory: the classification problem for…
The entangled quantum states play a key role in quantum information. The association of the quantum state vector with each individual physical system in an attributive way is a source of many false paradoxes and inconsistencies. The…
Entangled physical systems are an important resource in quantum information. Some authors claim that in fact all quantum states are entangled. In this paper we show that this claim is incorrect and we discuss in operational way differences…
The concept of intrinsic and operational observables in quantum mechanics is introduced. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the…
A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting in each round, as well as the final score of the…
One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision making, based on the mathematical theory of separable Hilbert spaces.…
A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only feature known before an experiment is performed are the probabilities for various events to occur. The sum of the…