Related papers: Non-classical conditional probability and the quan…
We formulate a Born rule for families of quantum systems parametrized by a noncommutative space of control parameters. The resulting formalism may be viewed as a generalization of quantum mechanics where overlaps take values in a…
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases.…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…
We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing…
No-Cloning and No-Deleting theorems are verified with the constraint on local state transformations via the existence of incomparable states. Assuming the existence of exact cloning or deleting operation defined on a minimum number of two…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
The no-masking theorem states that it is impossible to encode an arbitrary quantum state into the correlations between two subsystems so that no original information about is accessible in the marginal state of either subsystem. In this…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
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…
A new algorithm for estimating the fraction of numbers that is present in a superpositional state which satisfies a given condition,is introduced.This algorithm is conceptually simple and does not require quantum Fourier transform.Also the…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for…
The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: the standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and…
Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities.…
Probabilistically creating n perfect clones from m copies for one of N priori known quantum states with minimum failure probability is a long-standing problem. We provide a rigorous proof for the geometric approach to this probabilistic…
Over the past decade quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed the very idea of viewing quantum states as carriers of…
The auxiliary rules of quantum mechanics have always included the Born rule that connects probability with square modulus. This need not be the case, for it is possible to introduce probability into the theory through probability current…
We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of the statistical length of a state. Its statistical nature…