9 research outputs found
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
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
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
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 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