Related papers: On Composite Quantum Hypothesis Testing
The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum…
The task of binary quantum hypothesis testing is to determine the state of a quantum system via measurements on it, given the side information that it is in one of two possible states, say $\rho$ and $\sigma$. This task is generally studied…
This work explores connections between the quantum relative entropy of two faithful states $\rho,\sigma$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $\mu,\nu$. Here, $\mu$ and $\nu$ are…
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
We generalize recent work of Massar and Popescu dealing with the amount of classical data that is produced by a quantum measurement on a quantum state ensemble. In the previous work it was shown how spurious randomness generally contained…
Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
We consider a distributed quantum hypothesis testing problem with communication constraints, in which the two hypotheses correspond to two different states of a bipartite quantum system, multiple identical copies of which are shared between…
According to Popescu's recent analysis [Phys. Rev. Lett. {\bf72}, 797 (1994)], {\it nonideal} measurements, rather than ideal ones, may be more sensitive to reveal nonlocal correlations between distant parts of composite quantum systems.…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
We address the challenge of certifying quantum behavior with single macroscopic massive particles, subject to decoherence and finite data. We propose a hypothesis testing framework that distinguishes between classical and quantum mechanics…
Compact expressions for the average subentropy and coherence are obtained for random mixed states that are generated via various probability measures. Surprisingly, our results show that the average subentropy of random mixed states…
The direct part of Stein's lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein's…
Given two pairs of quantum states, we want to decide if there exists a quantum channel that transforms one pair into the other. The theory of quantum statistical comparison and quantum relative majorization provides necessary and sufficient…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
We present two general approaches to obtain the strong converse rate of quantum hypothesis testing for correlated quantum states. One approach requires that the states satisfy a certain factorization property; typical examples of such…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…