104 research outputs found
Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
We calculate a nonequilibrium steady state of a quantum XX chain in the
presence of dephasing and driving due to baths at chain ends. The obtained
state is exact in the limit of weak driving while the expressions for one- and
two-point correlations are exact for an arbitrary driving strength. In the
steady state the magnetization profile and the spin current display diffusive
behavior. Spin-spin correlation function on the other hand has long-range
correlations which though decay to zero in either the thermodynamical limit or
for equilibrium driving. At zero dephasing a nonequilibrium phase transition
occurs from a ballistic transport having short-range correlations to a
diffusive transport with long-range correlations.Comment: 5 page
Quantum freeze of fidelity decay for chaotic dynamics
We show that the mechanism of quantum freeze of fidelity decay for
perturbations with zero time-average, recently discovered for a specific case
of integrable dynamics [New J. Phys. 5 (2003) 109], can be generalized to
arbitrary quantum dynamics. We work out explicitly the case of chaotic
classical counterpart, for which we find semi-classical expressions for the
value and the range of the plateau of fidelity. After the plateau ends, we find
explicit expressions for the asymptotic decay, which can be exponential or
Gaussian depending on the ratio of the Heisenberg time to the decay time.
Arbitrary initial states can be considered, e.g. we discuss coherent states and
random states.Comment: 4 pages, 3 ps figures ; v2 corrected mistake in formula for t_
Optimal two-qubit gate for generation of random bipartite entanglement
We numerically study protocols consisting of repeated applications of two
qubit gates used for generating random pure states. A necessary number of steps
needed in order to generate states displaying bipartite entanglement typical of
random states is obtained. For generic two qubit entangling gate the decay rate
of purity is found to scale as and therefore of order steps
are necessary to reach random bipartite entanglement. We also numerically
identify the optimal two qubit gate for which the convergence is the fastest.
Perhaps surprisingly, applying the same good two qubit gate in addition to a
random single qubit rotations at each step leads to a faster generation of
entanglement than applying a random two qubit transformation at each step.Comment: 9 pages, 9 PS figures; published versio
Entanglement of random vectors
We analytically calculate the average value of i-th largest Schmidt
coefficient for random pure quantum states. Schmidt coefficients, i.e.,
eigenvalues of the reduced density matrix, are expressed in the limit of large
Hilbert space size and for arbitrary bipartite splitting as an implicit
function of index i.Comment: 8 page
Initial-state randomness as a universal source of decoherence
We study time evolution of entanglement between two qubits, which are part of
a larger system, after starting from a random initial product state. We show
that, due to randomness in the initial product state, entanglement is present
only between directly coupled qubits and only for short times. Time dependence
of the entanglement appears essentially independent of the specific hamiltonian
used for time evolution and is well reproduced by a parameter-free two-body
random matrix model.Comment: 8 pages, 6 figure
Crossover between ballistic and diffusive transport: The Quantum Exclusion Process
We study the evolution of a system of free fermions in one dimension under
the simultaneous effects of coherent tunneling and stochastic Markovian noise.
We identify a class of noise terms where a hierarchy of decoupled equations for
the correlation functions emerges. In the special case of incoherent,
nearest-neighbour hopping the equation for the two-point functions is solved
explicitly. The Green's function for the particle density is obtained
analytically and a timescale is identified where a crossover from ballistic to
diffusive behaviour takes place. The result can be interpreted as a competition
between the two types of conduction channels where diffusion dominates on large
timescales.Comment: 20 pages, 5 figure
Detecting entanglement of random states with an entanglement witness
The entanglement content of high-dimensional random pure states is almost
maximal, nevertheless, we show that, due to the complexity of such states, the
detection of their entanglement using witness operators is rather difficult. We
discuss the case of unknown random states, and the case of known random states
for which we can optimize the entanglement witness. Moreover, we show that
coarse graining, modeled by considering mixtures of m random states instead of
pure ones, leads to a decay in the entanglement detection probability
exponential with m. Our results also allow to explain the emergence of
classicality in coarse grained quantum chaotic dynamics.Comment: 14 pages, 4 figures; minor typos correcte
Eigenlevel statistics of the quantum adiabatic algorithm
We study the eigenlevel spectrum of quantum adiabatic algorithm for
3-satisfiability problem, focusing on single-solution instances. The properties
of the ground state and the associated gap, crucial for determining the running
time of the algorithm, are found to be far from the predictions of random
matrix theory. The distribution of gaps between the ground and the first
excited state shows an abundance of small gaps. Eigenstates from the central
part of the spectrum are, on the other hand, well described by random matrix
theory.Comment: 8 pages, 10 ps figure
Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
Explicit solution for the 2-point correlation function in a non-equilibrium
steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in
the Lindblad formulation is provided. A non-equilibrium quantum phase
transition from exponentially decaying correlations to long-range order is
discussed analytically. In the regime of long-range order a new phenomenon of
correlation resonances is reported, where the correlation response of the
system is unusually high for certain discrete values of the external bulk
parameter, e.g. the magnetic field.Comment: 20 Pages, 5 figure
- …