相关论文: Optimal measurements for the dihedral hidden subgr…
We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.
Let $X$ be a set of items of size $n$ that contains some defective items, denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The outcome of a test is $1$ if $Q$ contains at least…
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
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…
In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a…
Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…
Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…
We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…
The abelian Hidden Subgroup Problem (HSP) is extremely general, and many problems with known quantum exponential speed-up (such as integers factorisation, the discrete logarithm and Simon's problem) can be seen as specific instances of it.…
Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete…
We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only sequential measurements are allowed. Sequential measurements from…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
A quantum ensemble $\{(p_x, \rho_x)\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a…
In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure…
It is shown that different distinguishability measures impose different orderings on ensembles of $N$ pure quantum states. This is demonstrated using ensembles of equally-probable, linearly independent, symmetrical pure states, with the…
In the long-studied problem of combinatorial group testing, one is asked to detect a set of $k$ defective items out of a population of size $n$, using $m \ll n$ disjunctive measurements. In the non-adaptive setting, the most widely used…
To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…
In this paper, a new method for investigating Dirichlet's divisor problem is developed. For this purpose, integer points under the graph of a hyperbola are studied. Since many investigations in this direction focus on direct estimates of…