Related papers: Composite systems and state transformations in top…

The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…

We apply a Bayesian data analysis scheme known as the Markov Chain Monte Carlo (MCMC) to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical…

There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…

The characterization of information within a multiparty system is both significant and complex. This paper presents the concept of generalized conditional mutual information, along with a family of multiparty quantum mutual information…

We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible…

In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi-qubit states in terms of these schemes and also discuss…

We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal algorithm, whose prototype is the state reduction algorithm…

We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…

We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry…

One of the fundamental features of quantum mechanics is the superposition principle, a manifestation of which is embodied in quantum coherence. Coherence of a quantum state is invariably defined with respect to a preferred set of pointer…

We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…

The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…

This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…

In the classical domain, it is well-known that divisibility does not imply that a stochastic process is Markovian. However, for quantum processes, divisibility is often considered to be synonymous with Markovianity. We show that completely…

The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…

An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…

We present a probabilistic quantum algorithm for preparing mixed states which, in expectation, are proportional to the solutions of Lyapunov equations -- linear matrix equations ubiquitous in the analysis of classical and quantum dynamical…

According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov's axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the…

We propose to characterize multipartite entanglement of pure states as local unitary transformations acting on some parts of a system that can be undone by local unitary transformations acting on other parts. This leads to a definition of…

Recently, some attention has been paid to falsifying the Leggett model, in which global probabilities characterizing a quantum state are represented by a combination of factorisable distributions. This idea was even verified in experiments,…