Related papers: Positive operator-valued measures in quantum decis…
Negative probabilities have long been discussed in connection with the foundations of quantum mechanics. We have recently shown that, if signed measures are allowed on the hidden variables, the class of probability models which can be…
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…
We find that a class of entanglement measures for bipartite pure state can be expressed by the average values of quantum operators, which are related to any complete basis of one partite operator space. Two specific examples are given based…
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
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…
Quantum entanglement is a key physical resource in quantum information processing that allows for performing basic quantum tasks such as teleportation and quantum key distribution, which are impossible in the classical world. Ever since the…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
Quantum entanglement lies at the heart of quantum mechanics in both fundamental and practical aspects. The entanglement of quantum states has been studied widely, however, the entanglement of operators has not been studied much in spite of…
To optimize the entanglement detection, we formulate the metrologically operational entanglement condition in quantum Fisher information by maximizing the QFI on the measurement orbit. Specifically, we consider two classes of typical local…
We study the quantum moment problem: Given a conditional probability distribution together with some polynomial constraints, does there exist a quantum state rho and a collection of measurement operators such that (i) the probability of…
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…
We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics…
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent,…
The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum…
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…