Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems. It is also useful in quantum information applications, such as the characterisation of… (More)
There are hamiltonians that solve a search problem of finding one of N items in O(√ N) steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamil-tonian, Hg. Then the known search hamiltonians become special cases of Hg. From the generalized search hamiltonian, we present remarkable… (More)
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of… (More)
We investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics.
Farhi et al. suggested the analogue quantum search Hamiltonian and Fenner also proposed the intuitive quantum search Hamiltonian. Recently the generalized quantum search Hamiltonian containning hamiltonians of Farhi et al. and Fenner was presented in quant-ph/0110020. In this letter, we analyze the running time of the generalized quantum search Hamiltonian.… (More)
In this letter, we show that the laser Hamiltonian can perform the quantum search. We also show that the process of quantum search is a resonance between the initial state and the target state, which implies that Nature already has a quantum search system to use a transition of energy. In addition, we provide the particular scheme to implement the quantum… (More)
Quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving instances of NP-complete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential to examine the minimum energy gap between the ground level and the next one through the evolution. In this letter, we… (More)