Related papers: Partially smoothed information measures
Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…
This study revisits label smoothing via a form of information bottleneck. Under the assumption of sufficient model flexibility and no conflicting labels for the same input, we theoretically and experimentally demonstrate that the model…
I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the…
One of the predominant challenges when engineering future quantum information processors is that large quantum systems are notoriously hard to maintain and control accurately. It is therefore of immediate practical relevance to investigate…
We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a…
A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in…
Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
State smoothing is a technique to estimate a state at a particular time, conditioned on information obtained both before (past) and after (future) that time. For a classical system, the smoothed state is a normalized product of the…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
Quantum initial state estimation through entanglement and continuous measurement is introduced. This paper provides a unified formulation of classical and quantum smoothing and shows a smoothing uncertainty relation. As an example, a…
In this paper we investigate the problem of controlling a partially observed stochastic dynamical system such that its state is difficult to infer using a (fixed-interval) Bayesian smoother. This problem arises naturally in applications in…
We study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the smoother entropy, which is the conditional…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
Although quantum entanglement has already been verified experimentally and applied in quantum computing, quantum sensing and quantum networks, most of the existing measures cannot characterize the entanglement faithfully. In this work, by…
Entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von Neumann entropy of the reduced states of either of its subsystems. The measure is established under entanglement…
Quantum state smoothing is a technique to estimate an unknown true state of an open quantum system based on partial measurement information both prior and posterior to the time of interest. In this paper, we show that the smoothed quantum…
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play a crucial role in information theory, signal processing and cryptography. We present various properties of smooth numbers…