9,593 research outputs found
Measuring entanglement in condensed matter systems
We show how entanglement may be quantified in spin and cold atom many-body
systems using standard experimental techniques only. The scheme requires no
assumptions on the state in the laboratory and a lower bound to the
entanglement can be read off directly from the scattering cross section of
Neutrons deflected from solid state samples or the time-of-flight distribution
of cold atoms in optical lattices, respectively. This removes a major obstacle
which so far has prevented the direct and quantitative experimental study of
genuine quantum correlations in many-body systems: The need for a full
characterization of the state to quantify the entanglement contained in it.
Instead, the scheme presented here relies solely on global measurements that
are routinely performed and is versatile enough to accommodate systems and
measurements different from the ones we exemplify in this work.Comment: 6 pages, 2 figure
A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
We prove that quantum many-body systems on a one-dimensional lattice locally
relax to Gaussian states under non-equilibrium dynamics generated by a bosonic
quadratic Hamiltonian. This is true for a large class of initial states - pure
or mixed - which have to satisfy merely weak conditions concerning the decay of
correlations. The considered setting is a proven instance of a situation where
dynamically evolving closed quantum systems locally appear as if they had truly
relaxed, to maximum entropy states for fixed second moments. This furthers the
understanding of relaxation in suddenly quenched quantum many-body systems. The
proof features a non-commutative central limit theorem for non-i.i.d. random
variables, showing convergence to Gaussian characteristic functions, giving
rise to trace-norm closeness. We briefly relate our findings to ideas of
typicality and concentration of measure.Comment: 27 pages, final versio
Scalable reconstruction of density matrices
Recent contributions in the field of quantum state tomography have shown
that, despite the exponential growth of Hilbert space with the number of
subsystems, tomography of one-dimensional quantum systems may still be
performed efficiently by tailored reconstruction schemes. Here, we discuss a
scalable method to reconstruct mixed states that are well approximated by
matrix product operators. The reconstruction scheme only requires local
information about the state, giving rise to a reconstruction technique that is
scalable in the system size. It is based on a constructive proof that generic
matrix product operators are fully determined by their local reductions. We
discuss applications of this scheme for simulated data and experimental data
obtained in an ion trap experiment.Comment: 9 pages, 5 figures, replaced with published versio
Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence
We demonstrate that the dynamics of an open quantum system can be calculated
efficiently and with predefined error, provided a basis exists in which the
system-environment interactions are local and hence obey the Lieb-Robinson
bound. We show that this assumption can generally be made. Defining a dynamical
renormalization group transformation, we obtain an effective Hamiltonian for
the full system plus environment that comprises only those environmental
degrees of freedom that are within the effective light cone of the system. The
reduced system dynamics can therefore be simulated with a computational effort
that scales at most polynomially in the interaction time and the size of the
effective light cone. Our results hold for generic environments consisting of
either discrete or continuous degrees of freedom
- …