1,598 research outputs found
Quantum state discrimination bounds for finite sample size
In the problem of quantum state discrimination, one has to determine by
measurements the state of a quantum system, based on the a priori side
information that the true state is one of two given and completely known
states, rho or sigma. In general, it is not possible to decide the identity of
the true state with certainty, and the optimal measurement strategy depends on
whether the two possible errors (mistaking rho for sigma, or the other way
around) are treated as of equal importance or not. Results on the quantum
Chernoff and Hoeffding bounds and the quantum Stein's lemma show that, if
several copies of the system are available then the optimal error probabilities
decay exponentially in the number of copies, and the decay rate is given by a
certain statistical distance between rho and sigma (the Chernoff distance, the
Hoeffding distances, and the relative entropy, respectively). While these
results provide a complete solution to the asymptotic problem, they are not
completely satisfying from a practical point of view. Indeed, in realistic
scenarios one has access only to finitely many copies of a system, and
therefore it is desirable to have bounds on the error probabilities for finite
sample size. In this paper we provide finite-size bounds on the so-called Stein
errors, the Chernoff errors, the Hoeffding errors and the mixed error
probabilities related to the Chernoff and the Hoeffding errors.Comment: 31 pages. v4: A few typos corrected. To appear in J.Math.Phy
A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions
We study a matrix product state (MPS) algorithm to approximate excited states
of translationally invariant quantum spin systems with periodic boundary
conditions. By means of a momentum eigenstate ansatz generalizing the one of
\"Ostlund and Rommer [1], we separate the Hilbert space of the system into
subspaces with different momentum. This gives rise to a direct sum of effective
Hamiltonians, each one corresponding to a different momentum, and we determine
their spectrum by solving a generalized eigenvalue equation. Surprisingly, many
branches of the dispersion relation are approximated to a very good precision.
We benchmark the accuracy of the algorithm by comparison with the exact
solutions of the quantum Ising and the antiferromagnetic Heisenberg spin-1/2
model.Comment: 13 pages, 11 figures, 5 table
Growth kinetics of environmental Legionella pneumophila isolated from industrial wastewater
Wastewater treatment plants are environmental niches for Legionella pneumophila, the most commonly identified causative agent of severe pneumonia known as Legionnaire's disease. In the present study, Legionella pneumophila's concentrations were monitored in an industrial wastewater treatment plant and environmental isolates were characterized concerning their growth kinetics with respect to temperature and their inhibition by organic acids and ammonium. The results of the monitoring study showed that Legionella pneumophila occurs in activated sludge tanks operated with very different sludge retention times, 2.5 days in a complete-mix reactor, and 10 days in a membrane bioreactor, indicating that this bacterium can grow at different rates, despite the same wastewater temperature of 35 degrees C. The morphology of Legionella cells is different in both reactors; in the membrane bioreactor, the bacteria grow in clusters, while in the complete-mix reactor, filaments predominate demonstrating a faster growth rate. Legionella pneumophila concentrations in the complete-mix reactor and in the membrane bioreactor were within the range 3 x 10(1) to 4.8 x 10(3) GU/mL and 3 x 10(2) to 4.7 x 10(3) GU/mL, respectively. Environmental Legionella pneumophila SG2-14 isolates showed distinct temperature preferences. The lowest growth rate was observed at 28 degrees C, and the highest 0.34 d(-1) was obtained at 42 degrees C. The presence of high concentrations of organic acids and ammonium found in anaerobically pre-treated wastewater caused growth inhibition. Despite the increasing research efforts, the mechanisms governing the growth of Legionella pneumophila in wastewater treatment plants are still unclear. New innovative strategies to prevent the proliferation of this bacterium in wastewater are in demand
Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
We consider the manifold of all quantum many-body states that can be
generated by arbitrary time-dependent local Hamiltonians in a time that scales
polynomially in the system size, and show that it occupies an exponentially
small volume in Hilbert space. This implies that the overwhelming majority of
states in Hilbert space are not physical as they can only be produced after an
exponentially long time. We establish this fact by making use of a
time-dependent generalization of the Suzuki-Trotter expansion, followed by a
counting argument. This also demonstrates that a computational model based on
arbitrarily rapidly changing Hamiltonians is no more powerful than the standard
quantum circuit model.Comment: Presented at QIP 201
Area law violations in a supersymmetric model
We study the structure of entanglement in a supersymmetric lattice model of
fermions on certain types of decorated graphs with quenched disorder. In
particular, we construct models with controllable ground state degeneracy
protected by supersymmetry and the choice of Hilbert space. We show that in
certain special limits these degenerate ground states are associated with local
impurities and that there exists a basis of the ground state manifold in which
every basis element satisfies a boundary law for entanglement entropy. On the
other hand, by considering incoherent mixtures or coherent superpositions of
these localized ground states, we can find regions that violate the boundary
law for entanglement entropy over a wide range of length scales. More
generally, we discuss various desiderata for constructing violations of the
boundary law for entanglement entropy and discuss possible relations of our
work to recent holographic studies.Comment: 20 pages, 1 figure, 1 appendi
Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement
Functionality in single-molecule devices: Model calculations and applications of the inelastic electron tunneling signal in molecular junctions
We analyze how functionality could be obtained within single-molecule devices
by using a combination of non-equilibrium Green's functions and ab-initio
calculations to study the inelastic transport properties of single-molecule
junctions. First we apply a full non-equilibrium Green's function technique to
a model system with electron-vibration coupling. We show that the features in
the inelastic electron tunneling spectra (IETS) of the molecular junctions are
virtually independent of the nature of the molecule-lead contacts. Since the
contacts are not easily reproducible from one device to another, this is a very
useful property. The IETS signal is much more robust versus modifications at
the contacts and hence can be used to build functional nanodevices. Second, we
consider a realistic model of a organic conjugated molecule. We use ab-initio
calculations to study how the vibronic properties of the molecule can be
controlled by an external electric field which acts as a gate voltage. The
control, through the gate voltage, of the vibron frequencies and (more
importantly) of the electron-vibron coupling enables the construction of
functionality: non-linear amplification and/or switching is obtained from the
IETS signal within a single-molecule device.Comment: Accepted for publication in Journal of Chemical Physic
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