Related papers: Non-classical conditional probability and the quan…
While the no-cloning theorem, which forbids the perfect copying of quantum states, is well-known as one of the defining features of quantum mechanics, the question of how well the theory allows a state to be cloned is yet to be completely…
Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
We investigate the consistency of conditional quantum probabilities. This is whether there is compatibility between the Kolmogorov-Bayes conditional probabilities and the Born rule. We show that they are not compatible in the sense that…
The nondistributivity of compound quantum mechanical propositions leads to a theorem that rules out the possibility of microscopic deterministic hidden variables, the Logical No-Go Theorem. We observe that there appear in fact two distinct…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
The impossibility to clone an unknown quantum state is a powerful principle to understand the nature of quantum mechanics, especially within the context of quantum computing and quantum information. This principle has been generalized to…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
The impossibility of perfect cloning and state estimation are two fundamental results in Quantum Mechanics. It has been conjectured that quantum cloning becomes equivalent to state estimation in the asymptotic regime where the number of…
Probabilistic quantum cloning and identifying machines can be constructed via unitary-reduction processes [Duan and Guo, Phys. Rev. Lett. 80, 4999 (1998)]. Given the cloning (identifying) probabilities, we derive an explicit representation…
The algebraic quantification of nonclassicality, which naturally arises from the quantum superposition principle, is related to properties of regular nonclassicality quasiprobabilities. The latter are obtained by non-Gaussian filtering of…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power? Although reasonable quantum random sources do not add computational power, the discussion of…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Quantum mechanics put restriction on performing some task which we can do classically. One such restriction is that we cannot copy an arbitrary quantum state. This is known as No-cloning theorem. Although quantum mechanics forbid us to…
Cloning, or approximate cloning, is one of basic operations in quantum information processing. In this paper, we deal with cloning of classical states, or probability distribution in asymptotic setting. We study the quality of the…