Related papers: The Shannon-entropy-based uncertainty relation for…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…
We explore connections between homotopy type theory and information theory through homotopy cardinality. We define probability types and random variable types, prove that homotopy cardinality respects dependent sums under truncation and…
We study an information-theoretic measure of uncertainty for quantum systems. It is the Shannon information $I$ of the phase space probability distribution $\la z | \rho | z \ra $, where $|z \ra $ are coherent states, and $\rho$ is the…
We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with…
The entanglement in a quantum system that possess an internal symmetry, characterized by the Sz-magnetization or U(1)-charge, is distributed among different sectors. The aim of this letter is to gain a deeper understanding of the…
We study the coherent dynamics of two interacting particles in a quantum double-well and show that the Shannon entropy can be a definitive signature of entanglement as an alternative to concur- rence, a connection not reported previously.…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this letter, we introduce a systematic method to construct a series of entropies,…
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3…
We highlight the advantages of using simultaneously the Shannon and Fisher information measures in providing a useful form of the uncertainty relation for the position-momentum case. It does not require any Fourier transformation. The…
This paper studies the uncertainty principle for spherical $h$-harmonic expansions on the unit sphere of $\mathbb{R}^d$ associated with a weight function invariant under a general finite reflection group, which is in full analogy with the…
We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
Quantum entropy is an important measure for describing the uncertainty of a quantum state, more uncertainty in subsystems implies stronger quantum entanglement between subsystems. Our goal in this work is to quantify bipartite entanglement…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
Uncertainty relation for photons that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in…
By revisiting the mathematical foundation of the uncertainty relation, skew information-based uncertainty sequences are developed for any two quantum channels. A reinforced version of the Cauchy-Schwarz inequality is adopted to improve the…