Quantum f -divergences are a quantum generalization of the classical notion of f divergences, and are a special case of Petz’ quasi-entropies. Many well-known distinguishability measures of quantum states are given by, or derived from, f -divergences; special examples include the quantum relative entropy, the Rényi relative entropies, and the Chernoff and Hoeffding measures. Here we show that t...

We adopt L1 distance as Eve’s distinguishability in secret key generation from a common random number without communication. Under this secrecy criterion, using the Rényi entropy of order 1 + s for s ∈ [0, 1], we derive a new upper bound of Eve’s distinguishability under the application of the universal2 hash function. It is also shown that this bound gives the tight exponential decreasing rate...

Interference effects are known to have a dependence upon indistinguishability of path. For this reason, it is accepted that different sources of a system cannot interfere if they have distinguishable states. We present an analysis of interference that predicts the allowance of interference between distinguishable states under the strict condition that the preparation has no distinguishability o...

Relativistic quantum field theory imposes additional fundamental restrictions on the distinguishability of quantum states. Because of the unavoidable delocalization of the quantum field states in the Minkowski space-time, the reliable (with unit probability) distinguishability of orthogonal states formally requires infinite time. For the cryptographic protocols which are finite in time the latt...

A central problem in ranking is to design a ranking measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the widely used Normalized Discounted Cumulative Gain (NDCG)-type ranking measures. Although there are extensive empirical studies of NDCG, little is known about its theoretical properties. We first show that, whatever the ranking function is, ...

A central problem in ranking is to design a measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the Normalized Discounted Cumulative Gain (NDCG) which is a family of ranking measures widely used in practice. Although there are extensive empirical studies of NDCG, little is known about its theoretical properties. We first show that, whatever the r...