Negativity as a distance from a separable state

The computable measure of the mixed-state entanglement, the negativity, is shown to admit a clear geometrical interpretation, when applied to Schmidt-correlated (SC) states: the negativity of a SC state equals a distance of the state from a pertinent separable state. As a consequence, a SC state is separable if and only if its negativity vanishes. Another remarkable consequence is that the negativity of a SC can be estimated "at a glance" on the density matrix. These results are generalized to mixtures of SC states, which emerge in certain quantum-dynamical settings.Comment: 9 pages, 1 figur

On the temperature dependence of the interaction-induced entanglement

Both direct and indirect weak nonresonant interactions are shown to produce entanglement between two initially disentangled systems prepared as a tensor product of thermal states, provided the initial temperature is sufficiently low. Entanglement is determined by the Peres-Horodeckii criterion, which establishes that a composite state is entangled if its partial transpose is not positive. If the initial temperature of the thermal states is higher than an upper critical value $T_{uc}$ the minimal eigenvalue of the partially transposed density matrix of the composite state remains positive in the course of the evolution. If the initial temperature of the thermal states is lower than a lower critical value $T_{lc}\leq T_{uc}$ the minimal eigenvalue of the partially transposed density matrix of the composite state becomes negative which means that entanglement develops. We calculate the lower bound $T_{lb}$ for $T_{lc}$ and show that the negativity of the composite state is negligibly small in the interval $T_{lb}<T<T_{uc}$. Therefore the lower bound temperature $T_{lb}$ can be considered as \textit{the} critical temperature for the generation of entanglement.Comment: 27 pages and 7 figure

Noise and Controllability: suppression of controllability in large quantum systems

A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? Complete controllability in practice requires that the effect of noise can be suppressed for an arbitrary transformation. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases, determined by the dimension of the Hilbert space representation of the algebra. We show that for large quantum systems, generic noise in the controls dominates for a typical class of target transformations i.e., complete controllability is destroyed by the noise.Comment: 4 pages, no figure

Efficient simulation of quantum evolution using dynamical coarse-graining

A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution, which can be interpreted as a process of weak measurement of the distinguished observables performed on the evolving system of interest. Given that the observables are "classical" and the Hamiltonian is moderately nonlinear, the open system dynamics displays a large time-scales separation between the dephasing of the observables and the decoherence of the evolving state in the basis of the generalized coherent states (GCS), associated with the spectrum-generating algebra. The time scale separation allows the unitary dynamics of the observables to be efficiently simulated by the open-system dynamics on the intermediate time-scale.The simulation employs unraveling of the corresponding master equations into pure state evolutions, governed by the stochastic nonlinear Schroedinger equantion (sNLSE). It is proved that GCS are globally stable solutions of the sNLSE, if the Hamilonian is linear in the algebra elements.Comment: The version submitted to Phys. Rev. A, 28 pages, 3 figures, comments are very welcom

Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities

We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine structure or displays a single asymmetric peak. For nano-mechanical resonators with a fluctuating number of attached molecules, the spectrum is found in a simple analytical form. The results bear on various types of systems where the reciprocal correlation time of frequency fluctuations can be comparable to the typical frequency jumps

The rise and fall of quantum and classical correlations in open-system dynamics

Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations -- entanglement. As a consequence, a local description of interacting quantum system is impossible as a rule. A unitarily evolving (isolated) quantum system generically develops extensive entanglement: the magnitude of the generated entanglement will increase without bounds with the effective Hilbert space dimension of the system. It is conceivable, that coupling of the interacting subsystems to local dephasing environments will restrict the generation of entanglement to such extent, that the evolving composite system may be considered as approximately disentangled. This conjecture is addressed in the context of some common models of a bipartite system with linear and nonlinear interactions and local coupling to dephasing environments. Analytical and numerical results obtained imply that the conjecture is generally false. Open dynamics of the quantum correlations is compared to the corresponding evolution of the classical correlations and a qualitative difference is found.Comment: 35 pages, 10 figures. Revised according to comments of the referees. Accepted for publication in Phys. Rev.

The possibility of improving procedures for quantitative threat assessment of unauthorized access to information of critical information infrastructure facilities

The content of the main threat assessment stages of unauthorized access (UA) at critical information infrastructure (CII) facilities is determined on the basis of analysis of the primary provisions of the Methodology for Assessing Information Security Threats, approved on February 5, 2021 by the FSTEC of Russia. The ways to develop a methodology for assessing such information security threats are focused. A functionally-oriented approach is proposed to take into account the dynamics of the UA threat implementation regarding information of CII facilities. The procedure for constructing a functional model of the threat is considered in accordance with its existing structuring within the framework of the basic model of information security threats presented in the documents of the FSTEC of Russia. The decompositional hierarchical structure of the target threat function is substantiated as the first stage in constructing the model. The content of structure levels is given: the level of target threat function, the level of its implementation strategies, the level of tactics used, the level of the intruder’s action stages, and the level of procedures done to access the operating environment of the computer system (CS) and destructive impact on information. The execution sequence of individual functional components of this structure is determined as well as the order of their implementation is illustrated in the form of a change of states of the Markov process as the second stage of constructing the model. Based on this vision, the possibility of moving from a description of the UA threat to information of CII facilities in terms of functional modeling to a mathematical representation of the temporal characteristics of functional components of its target function is demonstrated. The corresponding analytical expressions are given for various options for representing the order of executed functional components

The globally stable solution of a stochastic Nonlinear Schrodinger Equation

Weak measurement of a subset of noncommuting observables of a quantum system can be modeled by the open-system evolution, governed by the master equation in the Lindblad form. The open-system density operator can be represented as statistical mixture over non unitarily evolving pure states, driven by the stochastic Nonlinear Schrodinger equation (sNLSE). The globally stable solution of the sNLSE is obtained in the case where the measured subset of observables comprises the spectrum-generating algebra of the system. This solution is a generalized coherent state (GCS), associated with the algebra. The result is based on proving that GCS minimize the trace-norm of the covariance matrix, associated with the spectrum-generating algebra.Comment: 10 pages, comments are very welcom

A Complete Set of Local Invariants for a Family of Multipartite Mixed States

We study the equivalence of quantum states under local unitary transformations by using the singular value decomposition. A complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed states in KxMxN composite systems. Two density matrices in the same class are equivalent under local unitary transformations if and only if all these invariants have equal values for these density matrices.Comment: 10 page