Minimum-error state discrimination constrained by the no-signaling principle

Abstract

We provide a bound on the minimum error when discriminating among quantum states, using the no-signaling principle. The bound is general in that it depends on neither dimensions nor specific structures of given quantum states to be discriminated among. We show that the bound is tight for the minimum-error state discrimination between symmetric (both pure and mixed) qubit states. Moreover, the bound can be applied to a set of quantum states for which the minimum-error state discrimination is not known yet. Finally, our results strengthen the quantitative connection between two no-go theorems, the no-signaling principle and the no perfect state estimation.

Quantum state discrimination with general figures of merit

“…We first solved the problem for an even number of symmetric qubits with use of the no-signaling principle. Here both methods used for QSD [8][9][10][11] and QSE [12] are combined to get the solutions. We showed that, with use of the no-signaling principle, conditional probability always has the form α cos 2 (φ/2) + β.…”

“…(16). The bound reduces to P guess ≤ 1/(N p) when p i ≡ p [10]. The p in our case is calculated as p = 1/(1 + | r|| sin θ|) [10].…”

“…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.…”

“…That is, "no-signaling principle" can be replaced by "impossibility of discriminating two different decompositions of states corresponding to the same density operator" in Refs. [8][9][10][11][12] and throughout this paper. However, we adopt the no-signaling principle here because it makes the result more concrete.…”

“…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. Here both methods used for QSD [8][9][10][11] and QSE [12] are combined to get solutions. It turns out that optimal measurements are the same for all monotonous (symmetric) figures of merit in QSD.…”