We state a quantum version of the Bayes rule for statistical inference and give a simple
general derivation within the framework of generalized measurements. The rule can be …

Using the Shannon information theory and the Bayesian methodology for inverting quantum
data [KRW Jones, Ann. Phys.(NY) 207, 140 (1991)] we prove a fundamental bound upon the …

In this paper we address the problem of how much can be learned about an unknown
quantum state by a measurement. To this end we consider optimal measurements for the …

Knowing and guessing, these are two essential epistemological pillars in the theory of
quantum-mechanical measurement. As formulated quantum mechanics is a statistical …

We consider the problem of discriminating two different quantum states in the setting of
asymptotically many copies, and determine the minimal probability of error. This leads to the …

In the problem of quantum state discrimination, one has to determine by measurements the
state of a quantum system, based on the a priori side information that the true state is one of …

Abstract Braunstein and Caves (Braunstein SL and Caves CM 1994 Phys. Rev. Lett. 72
3439-43) proposed to use Helstrom's quantum information number to define, meaningfully, a …

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a
single trial, without any a priori connection to limiting frequencies. In this paper, we show …

Quantum-state reconstruction on a finite number of copies of a quantum system with
informationally incomplete measurements, as a rule, does not yield a unique result. We …

Hypothesis testing is a fundamental issue in statistical inference and has been a crucial
element in the development of information sciences. The Chernoff bound gives the minimal …