相关论文: Infinitely many constrained inequalities for the v…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
We provide a generalized treatment of uncertainties, von Neumann entropy, and squeezing in entangled bipartite pure state of two-level atoms. We observe that when the bipartite state is entangled, though the von Neumann entropy of the…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the…
We derive the strong subadditivity of the von Neumann entropy with a strict lower bound dependent on the distribution of quantum correlation in the system. We investigate the structure of states saturating the bounded subadditivity and…
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
We review the postulates of quantum mechanics that are needed to discuss the von Neumann's entropy. We introduce it as a generalization of Shannon's entropy and propose a simple game that makes easier understanding its physical meaning.
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
Let $S(\rho)=- Tr (\rho \log\rho)$ be the von Neumann entropy of an $N$-dimensional quantum state $\rho$ and $e_2(\rho)$ the second elementary symmetric polynomial of the eigenvalues of $\rho$. We prove the inequality $S(\rho) \le c(N)…
In 1997, Z.Zhang and R.W.Yeung found the first example of a conditional information inequality in four variables that is not "Shannon-type". This linear inequality for entropies is called conditional (or constraint) since it holds only…
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…
Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's…
We derive a universal inequality that provides a lower bound on the ensemble-averaged von Neumann entropy change in a quantum system subject to continuous measurement and dissipation. Our result clarifies how entropy production is…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
We investigate relations between the ranks of marginals of multipartite quantum states. These are the Schmidt ranks across all possible bipartitions and constitute a natural quantification of multipartite entanglement dimensionality. We…
Regarding the strange properties of quantum entropy and entanglement, e.g., the negative quantum conditional entropy, we revisited the foundations of quantum entropy, namely, von Neumann entropy, and raised the new method of quantum…
This paper presents self-contained proofs of the strong subadditivity inequality for quantum entropy and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps.…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…