2,548 research outputs found
Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity
We analytically determine the minimal time and the optimal control laws
required for the realization, up to an assigned fidelity and with a fixed
energy available, of entangling quantum gates () between
indirectly coupled qubits of a trilinear Ising chain. The control is coherent
and open loop, and it is represented by a local and continuous magnetic field
acting on the intermediate qubit. The time cost of this local quantum operation
is not restricted to be zero. When the matching with the target gate is perfect
(fidelity equal to one) we provide exact solutions for the case of equal Ising
coupling. For the more general case when some error is tolerated (fidelity
smaller than one) we give perturbative solutions for unequal couplings.
Comparison with previous numerical solutions for the minimal time to generate
the same gates with the same Ising Hamiltonian but with instantaneous local
controls shows that the latter are not time-optimal.Comment: 11 pages, no figure
On the Stability of a Stringy Black Hole
We study the stability under perturbations of a charged four dimensional
stringy black hole arising from gauging a previously studied WZW model. We find
that the black hole is stable only in the extremal case .Comment: 14 pages + 1 figure (not included but available on request
Optimal phase estimation and square root measurement
We present an optimal strategy having finite outcomes for estimating a single
parameter of the displacement operator on an arbitrary finite dimensional
system using a finite number of identical samples. Assuming the uniform {\it a
priori} distribution for the displacement parameter, an optimal strategy can be
constructed by making the {\it square root measurement} based on uniformly
distributed sample points. This type of measurement automatically ensures the
global maximality of the figure of merit, that is, the so called average score
or fidelity. Quantum circuit implementations for the optimal strategies are
provided in the case of a two dimensional system.Comment: Latex, 5 figure
Brachistochrone of Entanglement for Spin Chains
We analytically investigate the role of entanglement in time-optimal state
evolution as an appli- cation of the quantum brachistochrone, a general method
for obtaining the optimal time-dependent Hamiltonian for reaching a target
quantum state. As a model, we treat two qubits indirectly cou- pled through an
intermediate qubit that is directly controllable, which represents a typical
situation in quantum information processing. We find the time-optimal unitary
evolution law and quantify residual entanglement by the two-tangle between the
indirectly coupled qubits, for all possible sets of initial pure quantum states
of a tripartite system. The integrals of the motion of the brachistochrone are
determined by fixing the minimal time at which the residual entanglement is
maximized. Entan- glement plays a role for W and GHZ initial quantum states,
and for the bi-separable initial state in which the indirectly coupled qubits
have a nonzero value of the 2-tangle.Comment: 9 pages, 4 figure
The vacuum polarization around an axionic stringy black hole
We consider the effect of vacuum polarization around the horizon of a 4
dimensional axionic stringy black hole. In the extreme degenerate limit
(), the lower limit on the black hole mass for avoiding the polarization
of the surrounding medium is ( is the
proton mass), according to the assumed value of the axion mass (). In this case, there are no upper bounds on the mass
due to the absence of the thermal radiation by the black hole. In the
nondegenerate (classically unstable) limit (), the black hole always
polarizes the surrounding vacuum, unless the effective cosmological constant of
the effective stringy action diverges.Comment: 7 pages, phyzzx.tex, ROM2F-92-3
Bipolynomial Hilbert functions
Let X be a closed subscheme and let HF(X,-) and hp(X,-) denote, respectively,
the Hilbert function and the Hilbert polynomial of X. We say that X has
bipolynomial Hilbert function if HF(X,d)=min{hp(P^n,d),hp(X,d)} for every
non-negative integer d. We show that if X consists of a plane and generic
lines, then X has bipolynomial Hilbert function. We also conjecture that
generic configurations of non-intersecting linear spaces have bipolynomial
Hilbert function
Time-Optimal Transfer of Coherence
We provide exact analytical solutions for the problem of time-optimal
transfer of coherence from one spin polarization to a three-fold coherence in a
trilinear Ising chain with a fixed energy available and subject to local
controls with a non negligible time cost. The time of transfer is optimal and
consistent with a previous numerical result obtained assuming instantaneous
local controls.Comment: Published version (with typos in eqs. (25)-(27) corrected
A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the
dependence of the coefficients is nonlinear and nonlocal in time with respect
to the unknowns. We extend the numerical scheme proposed and studied recently
by the authors for a single FPK equation of this type. We analyse the
convergence of the scheme and we study its applicability in two examples. The
first one concerns a population model involving two interacting species and the
second one concerns two populations Mean Field Games
- …