14 research outputs found
Unambiguous discrimination between two unknown qudit states
We consider the unambiguous discrimination between two unknown qudit states
in -dimensional () Hilbert space. By equivalence of unknown
pure states to known mixed states and with the Jordan-basis method, we
demonstrate that the optimal success probability of the discrimination between
two unknown states is independent of the dimension . We also give a scheme
for a physical implementation of the programmable state discriminator that
unambiguously discriminate between two unknown states with optimal probability
of success.Comment: 8 pages, 3 figure
Quadrature-dependent Bogoliubov transformations and multiphoton squeezed states
We introduce a linear, canonical transformation of the fundamental
single--mode field operators and that generalizes the linear
Bogoliubov transformation familiar in the construction of the harmonic
oscillator squeezed states. This generalization is obtained by adding to the
linear transformation a nonlinear function of any of the fundamental quadrature
operators and , making the original Bogoliubov transformation
quadrature--dependent. Remarkably, the conditions of canonicity do not impose
any constraint on the form of the nonlinear function, and lead to a set of
nontrivial algebraic relations between the --number coefficients of the
transformation. We examine in detail the structure and the properties of the
new quantum states defined as eigenvectors of the transformed annihilation
operator . These eigenvectors define a class of multiphoton squeezed states.
The structure of the uncertainty products and of the quasiprobability
distributions in phase space shows that besides coherence properties, these
states exhibit a squeezing and a deformation (cooling) of the phase--space
trajectories, both of which strongly depend on the form of the nonlinear
function. The presence of the extra nonlinear term in the phase of the wave
functions has also relevant consequences on photon statistics and correlation
properties. The non quadratic structure of the associated Hamiltonians suggests
that these states be generated in connection with multiphoton processes in
media with higher nonlinearities.Comment: 16 pages, 15 figure
Engineering Entanglement between two cavity modes
We present scheme for generation of entanglement between different modes of
radiation field inside high-Q superconducting cavities. Our scheme is based on
the interaction of a three-level atom with the cavity field for pre-calculated
interaction times with each mode. This work enables us to generate complete set
of Bell basis states and GHZ state
Programmed discrimination of qbits with added classical information
We investigate some properties of programmed quantum-state discriminators with simple programs. Bergou et al. [Phys. Rev. A 73, 062334 (2006)] have considered programmable devices which are supplied with two distinct but unknown program qbits and one data qbit which is certain to be identical to one or other of the program qbits. The task is to discriminate between the first and the second possibility. In this paper, we consider this state-discrimination problem when there is some additional classical information available. We find that in the minimum error discrimination mode, the probability of correct discrimination is increased by each type of classical information. The same is broadly true of unambiguous discrimination, with the chance of success improving when the overlap between the program qbits is reduced
Quantum algorithm for the asymmetric weight decision problem and its generalization to multiple weights
As one of the applications of Grover search, an exact quantum algorithm for the symmetric weight decision problem of a Boolean function has been proposed recently. Although the proposed method shows a quadratic speedup over the classical approach, it only applies to the symmetric case of a Boolean function whose weight is one of the pair {0 < w1 < w2 < 1, w1 + w2 = 1}. In this article, we generalize this algorithm in two ways. Firstly, we propose a quantum algorithm for the more general asymmetric case where {0 < w1 < w2 < 1}. This algorithm is exact and computationally optimal. Secondly, we build on this to exactly solve the multiple weight decision problem for a Boolean function whose weight as one of {0 < w1 < w2 < … < wm < 1}. This extended algorithm continues to show a quantum advantage over classical methods. Thirdly, we compare the proposed algorithm with the quantum counting method. For the case with two weights, the proposed algorithm shows slightly lower complexity. For the multiple weight case, the two approaches show different performance depending on the number of weights and the number of solutions. For smaller number of weights and larger number of solutions, the weight decision algorithm can show better performance than the quantum counting method. Finally, we discuss the relationship between the weight decision problem and the quantum state discrimination problem
On quantum theory
10.1140/epjd/e2013-40486-5European Physical Journal D6711-EPJD