Related papers: Composite systems and state transformations in top…
An expansion of row Markov matrices in terms of matrices related to permutations with repetitions, is introduced.It generalises the Birkhoff-von Neumann expansion of doubly stochastic matrices in terms of permutation matrices (without…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
Figuring out the physical rationale behind natural selection of quantum theory is one of the most acclaimed quests in quantum foundational research. This pursuit has inspired several axiomatic initiatives to derive mathematical formulation…
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all $M$-sets, where $M$ is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way.…
Stochastic representation for interaction of quantum systems is formulated which allows to replace some of them by equivalent but purely commutative random sources. The formalism is applied to two-level systems interacting with Gaussian…
A definition of quantum correlation is presented for an arbitrary bipartite quantum state based on the skew information. This definition not only inherits the good properties of skew information such as the contractivity and so on, but also…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by…
The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…
We derive a classification and a measure of classical- and quantum-correlation of multipartite qubit, qutrit, and in general, $n$-level systems, in terms of SU$(n)$ representations of density matrices. We compare the measure for the case of…
Modal quantum theory (MQT) is a "toy model" of quantum theory in which amplitudes are elements of a general field. The theory predicts, not the probabilities of a measurement result, but only whether or not a result is possible. In this…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…
By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional quantum-to-classical transition.…