Related papers: Directed-completeness of quantum statistical exper…
We present an instance of a task of minimum-error discrimination of two qubit-qubit quantum channels for which a sequential strategy outperforms any parallel strategy. We then establish two new classes of strategies for channel…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
We present an alternative approach to the derivation of benchmarks for quantum channels, such as memory or teleportation channels. Using the concept of effective entanglement and the verification thereof, a testing procedure is derived…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies…
It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets…
A unified framework is proposed in this paper for parameter estimation using convex optimization and experiment design applying convex maximization for Pauli channels, that can be extended to generalized Pauli channels, too. In the case of…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
We introduce three metrics on the set of quantum probability measures over a compact Hausdorff space and characterize them in terms of the completely bounded norm of the corresponding unital completely positive maps. We extend the existing…
In this paper we shall introduce the mathematical framework for the description of measurements of quantum processes. Using this framework the process estimation problems can be treated in the similar way as the state estimation problems,…
Any reasonable measure of distinguishability of quantum states must satisfy a data processing inequality, that is, it must not increase under the action of a quantum channel. We can ask about the proportion of information lost or preserved…
Several communication models that are of relevance in practice are asymmetric in the way they act on the transmitted "objects". Examples include channels in which the amplitudes of the transmitted pulses can only be decreased, channels in…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
A number of atomic beam experiments, related to the Ramsey experiment and a recent experiment by Brune et al., are studied with respect to the question of complementarity. Three different procedures for obtaining information on the state of…
In classical statistics, a well known paradigm consists in establishing asymptotic equivalence between an experiment of i.i.d. observations and a Gaussian shift experiment, with the aim of obtaining optimal estimators in the former…
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…
The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back-action, the quantum state reconstruction is…
In theoretical machine learning, the statistical complexity is a notion that measures the richness of a hypothesis space. In this work, we apply a particular measure of statistical complexity, namely the Rademacher complexity, to the…
We study the problem of binary composite channel discrimination in the asymmetric setting, where the hypotheses are given by fairly arbitrary sets of channels, and samples do not have to be identically distributed. In the case of quantum…