Optimal quantum state estimation with use of the no-signaling principle

Abstract

A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independently of figures of merit, such as the fidelity or information gain. This proves that the optimal estimation for a quantum bit can be achieved by the same measurement for almost all figures of merit.

Quantum state discrimination with general figures of merit

“…Conditional probability of this case also gives maximal score. In the case of pure states, the optimal conditional probability is achieved by the uniform measurement, which thus becomes an optimal measurement [12]. In our case, however, we can expect that the conditional probability would have a more broad form because the states to be discriminated are mixed states and thus more nonorthogonal.…”

“…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.…”

“…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]. )…”