相关论文: A limit of the quantum Renyi divergence

Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…

Entanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an "area law" meaning the…

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…

In this article, we present quantum algorithms for estimating von Neumann entropy and Renyi entropy, which are crucial physical and information-theoretical properties of a given quantum state $\rho$. Although there have been existing works…

Quantum information decoupling is a fundamental quantum information processing task, which also serves as a crucial tool in a diversity of topics in quantum physics. In this paper, we characterize the reliability function of catalytic…

An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…

We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner-Popa index connects to sandwiched Renyi $p$-relative entropy for all $1/2\le p\le \infty$, including…

We investigate boundary critical phenomena from a quantum information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy S_alpha, which includes the von Neumann…

This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…

Entropy is one of the central quantities in thermodynamics, whose flow between two systems determines the statistics of energy transfers. In quantum systems entropy is non-linear in density matrix whose time evolution is cumbersome. Using…

We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of the space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for…

The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…

Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we…

Fidelity and relative entropy are two significant quantities in quantum information theory. We study the quantum fidelity and relative entropy under unitary orbits. The maximal and minimal quantum fidelity and relative entropy between two…

An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…

The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…

We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…

This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding, simplifying the analysis of quantum communication and state redistribution while…