Unambiguous discrimination between two unknown qudit states

We consider the unambiguous discrimination between two unknown qudit states in $n$-dimensional ($n\geqslant2$) 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 $n$. 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 $a$ and $a^{\dagger}$ 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 $X_{1}$ and $X_{2}$, 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 $c$--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 $b$. 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