4,810 research outputs found
A lower bound on the probability of error in quantum state discrimination
We give a lower bound on the probability of error in quantum state
discrimination. The bound is a weighted sum of the pairwise fidelities of the
states to be distinguished.Comment: 4 pages; v2 fixes typos and adds remarks; v3 adds a new referenc
On discontinuity waves and smooth waves in thermo-piezoelectric bodies
The solid body B under consideration is composed of a linear thermo-piezoelectric medium, i.e., a non-magnetizable linearly elastic dielectric medium that is heat
conducting and not electric conducting; B has a natural conguration, say a
placement of the three-dimensional Euclidean space that B can occupy
with zero stress, uniform temperature and uniform electric field. Such natural
conguration and state will be used as reference.
We consider processes of B constituted by small displacements, thermal
deviations and small electric fields
(u; T; E)
superposed to the reference state.
A smooth singular surface (or discontinuity surface) of order r in the triple
of fields (u; T; E) is referred to as a weak (thermo-piezoelectric) wave if r >=2.
Any singular surface of order r>= 2 is characteristic
(for the linear thermo-piezoelectric partial dierential equations).
Then smooth waves are considered.
(i) It is shown that the wavefront of a plane progressive wave is characteristic
if and only if the wave is isothermal.
(ii) The differential equations are characterized for standing waves of a
general type and for the standing waves which are sinusoidal. The latter are
isothermal, isentropic, have wavefronts which are characteristic, and their directions of propagation satisfy certain constitutive conditions.
(iii) The differential equations for plane progressive waves which are reversible
in time are characterized
Quantum walk speedup of backtracking algorithms
We describe a general method to obtain quantum speedups of classical
algorithms which are based on the technique of backtracking, a standard
approach for solving constraint satisfaction problems (CSPs). Backtracking
algorithms explore a tree whose vertices are partial solutions to a CSP in an
attempt to find a complete solution. Assume there is a classical backtracking
algorithm which finds a solution to a CSP on n variables, or outputs that none
exists, and whose corresponding tree contains T vertices, each vertex
corresponding to a test of a partial solution. Then we show that there is a
bounded-error quantum algorithm which completes the same task using O(sqrt(T)
n^(3/2) log n) tests. In particular, this quantum algorithm can be used to
speed up the DPLL algorithm, which is the basis of many of the most efficient
SAT solvers used in practice. The quantum algorithm is based on the use of a
quantum walk algorithm of Belovs to search in the backtracking tree. We also
discuss how, for certain distributions on the inputs, the algorithm can lead to
an exponential reduction in expected runtime.Comment: 23 pages; v2: minor changes to presentatio
The quantum complexity of approximating the frequency moments
The 'th frequency moment of a sequence of integers is defined as , where is the number of times that occurs in the
sequence. Here we study the quantum complexity of approximately computing the
frequency moments in two settings. In the query complexity setting, we wish to
minimise the number of queries to the input used to approximate up to
relative error . We give quantum algorithms which outperform the best
possible classical algorithms up to quadratically. In the multiple-pass
streaming setting, we see the elements of the input one at a time, and seek to
minimise the amount of storage space, or passes over the data, used to
approximate . We describe quantum algorithms for , and
in this model which substantially outperform the best possible
classical algorithms in certain parameter regimes.Comment: 22 pages; v3: essentially published versio
A Green-Naghdi approach for thermo-electroelasticity
The constitutive relations of piezoelectric ceramics are essentially nonlinear since the so-called piezoelectric moduli depend on the induced strains.
Pioneering papers in these topics dealt mainly with the isothermal case. In view of applications, however, thermal effects have to be taken into account in connection with thermo-electric behaviors.
Here we briefly compare continuum theories for nonlinear thermoelettroelasticity.
In particular we describe an extension of Green-Naghdi thermoelasticity theory for an electrically polarizable and finitely deformable heat conducting elastic continuumn, which interacts with the electric field.
In this theory, unlike other, thermal waves propagate at a finite speed
On the propagation of plane waves in piezoelectromagnetic monoclinic crystals
In a piezoelectromagnetic crystalline medium belonging to the class 2 of the
monoclinic crystallographic system we find some classes of piezoelectricity-induced
electromagnetic waves. These are time harmonic plane waves propagating along the
symmetry axis and depending only on the axial coordinate. There are two indepen-
dent modes of propagation, one longitudinal and one transverse, with mechanical
and electromagnetical couplings. The transverse mode admits as a particular case an
electromagnetic wave with no associated elastic deformation
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