Related papers: Efficient Optimal Minimum Error Discrimination of …
A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by M. Hayashi in terms of an infinite set of covariant…
We introduce random matrix theory to study the tomographic efficiency of a wide class of measurements constructed out of weighted 2-designs, including symmetric informationally complete (SIC) probability operator measurements (POMs). In…
In this paper we consider the optimal discrimination of two mixed qubit states for a measurement that allows a fixed rate of inconclusive results(FRIR). Our strategy for the problem is to transform the FRIR of two qubit states into a…
Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements…
We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the…
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…
The minimum-error probability of ambiguous discrimination for two quantum states is the well-known {\it Helstrom limit} presented in 1976. Since then, it has been thought of as an intractable problem to obtain the minimum-error probability…
Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states--the quantum states of light emitted by a laser--has immense practical importance. However, quantum mechanics imposes a…
This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations,…
The discrimination of quantum processes, including quantum states, channels, and superchannels, is a fundamental topic in quantum information theory. It is often of interest to analyze the optimal performance that can be achieved when…
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact…
We investigate quantum state discrimination with confidentiality. $N$ observers share a given quantum state belonging to a finite set of known states. The observers want to determine the state as accurately as possible and send a…
A suitable generalized measurement described by a 4-element positive operator-valued measure (POVM) on each particle of a two-qubit system in the singlet state is, from the point of view of Einstein, Podolsky, and Rosen's (EPR's) criterion…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
Positive operator valued measures (POVMs) are presented that allow an unknown pure state of a spin-1 particle to be determined with optimal fidelity when 2 to 5 copies of that state are available. Optimal POVMs are also presented for a…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
The problem of an optimal mapping between Hilbert spaces $IN$ and $OUT$, based on a series of density matrix mapping measurements $\rho^{(l)} \to \varrho^{(l)}$, $l=1\dots M$, is formulated as an optimization problem maximizing the total…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In…
Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task…
Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued…