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Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…
In this paper we investigate the connection between quantum information theory and machine learning. In particular, we show how quantum state discrimination can represent a useful tool to address the standard classification problem in…
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,…
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…
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.
Multiple-copy state discrimination is a fundamental task in quantum information processing. If there are two, pure, non-orthogonal states then both local and collective schemes are known to reach the Helstrom bound, the maximum probability…
Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another.…
We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to…
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…
Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an…
Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These…
Quantum state discrimination is a fundamental information processing task that serves as a building block for numerous applications and provides implications at the foundational level. In this work, we consider minimum error discrimination…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
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…
The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability for the state discrimination is known to be given by the Helstrom bound. A…
The problem of discriminating the state of a quantum system among a number of hypothetical states is usually addressed under the assumption that one has perfect knowledge of the possible states of the system. In this thesis, I analyze the…
Quantum state discrimination is one of the most fundamental problems studied in quantum information theory. Applications range from channel coding to metrology and cryptography. In this work, we introduce a new variant of this task: Local…
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate `high-level' theory and glued together self-consistently by a less accurate `low-level' theory at the…