Related papers: Optimal state discrimination and unstructured sear…
Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation, and predicting non-linear…
In this paper, we study the quantum-state estimation problem in the framework of optimal design of experiments. We first find the optimal designs about arbitrary qubit models for popular optimality criteria such as A-, D-, and E-optimal…
The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the…
A method for the study of steady-state nonlinear modes for Gross-Pitaevskii equation (GPE) is described. It is based on exact statement about coding of the steady-state solutions of GPE which vanish as $x\to+\infty$ by reals. This allows to…
Given a unitary representation of a finite group on a finite-dimensional Hilbert space, we show how to find a state whose translates under the group are distinguishable with the highest probability. We apply this to several quantum oracle…
This is a less technical presentation of the ideas in quant-ph/9804035 [Phys Rev Lett 83 (1999), 1707-1710]. A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
A fundamental problem in Quantum Information Processing is the discrimination amongst a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
We present an application of particle statistics to the problem of optimal ambiguous discrimination of quantum states. The states to be discriminated are encoded in the internal degrees of freedom of identical particles, and we use the…
We present a general scheme to realize the POVMs for the unambiguous discrimination of quantum states. For any set of pure states it enables us to set up a feasible linear optical circuit to perform their optimal discrimination, if they are…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental realisation. Inspired by these important research achievements, a conceptually simple approach is…
Entangled states, like the two-mode squeezed vacuum state, are known to give quantum advantage in the illumination protocol, a method to detect a weakly reflecting target submerged in a thermal background. We use non-Gaussian photon-added…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
We experimentally demonstrate an unambiguous quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal ($\mathcal{PT}$) symmetry in a single trapped $^{40}$Ca$^+$ ion. We show that any two…