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Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…

This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…

General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…

The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor…

We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states…

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds…

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…

A causal structure is a description of the functional dependencies between random variables. A distribution is compatible with a given causal structure if it can be realized by a process respecting these dependencies. Deciding whether a…

A symmetry in quantum mechanics is described by the projective representations of a Lie symmetry group that transforms between physical quantum states such that the square of the modulus of the states is invariant. The Heisenberg…

In this paper we provide a novel strategy to prove the validity of Hartree's theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the well-known case of trapped Bose gases, this can be shown using the…

Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product…

We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…

We argue that if de Sitter space is indeed represented by a finite dimensional quantum system, then semi-classical considerations, combined with the fundamental principles of quantum measurement theory, imply that any theoretical model of…

Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…

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 estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…

Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators. In general, this limits their reliability for strongly correlated systems, for instance, in…

We describe a purely algebraic method for finding the best separable approximation to a mixed state of a composite 2x2 quantum system, consisting of a decomposition of the state into a linear combination of a mixed separable part and a pure…