No-Signaling Principle Can Determine Optimal Quantum State Discrimination

Abstract

We provide a general framework of utilizing the no-signaling principle in derivation of the guessing probability in the minimum-error quantum state discrimination. We show that, remarkably, the guessing probability can be determined by the no-signaling principle. This is shown by proving that, in the semidefinite programing for the discrimination, the optimality condition corresponds to the constraint that quantum theory cannot be used for a superluminal communication. Finally, a general bound to the guessing probability is presented in a closed form.

Quantum state discrimination with general figures of merit

“…Proposition-2 [11]. From the no-signaling principle, the guessing probability in any state discriminator must be bounded as…”

“…Recently it has been shown that the no-signaling (no * Email: wyhwang@jnu.ac.kr superluminal communication) principle can greatly simplify analysis in quantum information [6,7] including analysis of QSD [8][9][10][11] and QSE [12]. In this paper, we consider the problem of the "QSD with general figures of merit", for an even number 2M , of symmetric states of quantum bits (qubits), with use of the no-signaling principle.…”

How to device-independently generate states for which unambiguous state discrimination is impossible

“…However, our method is not based on Bell's inequality, but on the no-signaling principle. (Communication scenario similar to the one considered here was proposed by Herbert [13] and was then applied to derive several bounds in quantum information, including approximate quantum cloning [14], quantum state discrimination [15,16], and quantum state estimation [17]. )…”

Optimal quantum state discrimination via nested binary measurements

“…The discrimination of quantum states [1] is one of the fundamental problems in Quantum Information and a basic task for several applications in communication [2][3][4][5][6], cryptography [7][8][9], fundamental questions [10][11][12][13], measurement and control [14,15] and algorithms [16]. Triggered by the observation that non-orthogonal quantum states cannot be perfectly discriminated, this subject has stimulated much work, both from a theoretical and practical point of view: the seminal works of Helstrom [17], Holevo [18] and Yuen et al [19] formalized the problem, obtaining a set of conditions for the optimal measurement operators, which in turn provide the optimal success probability, then solved it for sets of states symmetric under a unitary transformation; more recently, acknowledging that a general analytical solution is hard to find, research focused on finding a solution for sets with more general symmetries [20][21][22], computing explicitly the optimal measurements for the most interesting sets of states [23][24][25][26][27] and studying the implementation of such measurements with available technology (see for example [28][29][30][31][32][33][34][35][36][37][38][39][40] for the case of two ...…”