Related papers: A de Finetti representation for finite symmetric q…
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In…
We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…
We analyze general aspects of exchangeable quantum stochastic processes, as well as some concrete cases relevant for several applications to Quantum Physics and Probability. We establish that there is a one-to-one correspondence between…
The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e.~basis-independent, notion of dimensionality for ensembles of quantum states. It is…
We consider a class (convex set) of quantum states containing all finite rank states and infinite rank states with the sufficient rate of decreasing of eigenvalues (in particular, all Gaussian states). Quantum states from this class are…
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems…
Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis the…
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
In the realm of a quantum cosmological model for dark energy in which we have been able to construct a well-defined Hilbert space, a consistent coherent state representation has been formulated that may describe the quantum state of the…
In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This…
We formulate N-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix 2-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems,…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For…
Necessary and sufficient observable conditions for the nonnegativity of all partial transpositions of multi-mode quantum states are derived. The result is a hierarchy of inequalities for minors in terms of moments of the given state.…
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is…
We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation with magic states, the size of this state space only depends…
Everett's concept of relative state can be viewed as a map that contains information about correlations between measurement outcomes on two quantum systems. We demonstrate how geometric properties of the relative state map can be used to…
Multi-mode entangled coherent states are important resources for linear optics quantum computation and teleportation. Here we introduce the generalized balanced N-mode coherent states which recast in the multi-qudit case. The necessary and…