Related papers: Hidden Quantum Correlations in Single Qudit System…
While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and non-locality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the…
The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
Quantum dynamics that explore an unexpectedly small fraction of Hilbert space is inherently interesting. Integrable systems, quantum scars, MBL, hidden tensor structures, and systems with gauge symmetries are examples. Beyond dimension and…
Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, $X$-state, Werner state are studied in details. The…
We consider a problem of description of quantum correlations and dispersions of subsystems of complex open systems. Based on our previous results we proposed a method to evaluate pure quantum contributions from total statistical…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics…
We prove that the Hilbert space description of all joint von Neumann measurements on a quantum state can be reproduced in terms of a single measure space ({\Omega}, F, {\mu}) with a normalized real-valued measure {\mu}, that is, in terms of…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By…
Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear…
The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…
Given a collection $\{\lambda_1, \dots, \lambda_n\} $ of real numbers, there is a canonical probability distribution on the set of real symmetric or complex Hermitian matrices with eigenvalues $\lambda_1,\ldots,\lambda_n$. In this paper, we…
We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like…