Related papers: Algebraic Structure of the Minimum Error Discrimin…
We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of…
This paper considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
To analyze whole-genome genetic data inherited in families, the likelihood is typically obtained from a Hidden Markov Model (HMM) having a state space of 2^n hidden states where n is the number of meioses or edges in the pedigree. There…
We address the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem…
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by…
Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which…
In this paper, we treat a local discrimination problem in the framework of asymmetric hypothesis testing. We choose a known bipartite pure state $\ket{\Psi}$ as an alternative hypothesis, and the completely mixed state as a null hypothesis.…
Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
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…
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…
Evaluating the amount of information obtained from non-orthogonal quantum states is an important topic in the field of quantum information. The commonly used evaluation method is Holevo bound, which only provides a loose upper bound for…
This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…
We present reduction theorems for the problem of optimal unambiguous state discrimination (USD) of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank $n$ and are…
We study the distinguishability of quantum states under local operations with classical communication (LOCC), separable, and positive-partial-transpose (PPT) measurements, focusing on locally diagonal orthogonally invariant (LDOI) states --…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density…
Quantum linear optics without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some applications require entangled resources that are difficult to prepare. Thus, we…
We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary $m$ mixed quantum states with given prior probabilities. When $m=2$, this bound is precisely the well-known Helstrom…