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The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory.…
It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann…
The Renyi entropy coprises a group of data estimates that sums up the well-known Shannon entropy, acquiring a considerable lot of its properties. It appears as unqualified and restrictive entropy, relative entropy, or common data, and has…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
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…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…
The von Neumann entropy of a quantum state is a central concept in physics and information theory, having a number of compelling physical interpretations. There is a certain perspective that the most fundamental notion in quantum mechanics…
We investigate the universal inequalities relating the alpha-Renyi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropy (alpha=1) which are known to…
In [Berta et al., J. Math. Phys. 56, 022205 (2015)], we recently proposed Renyi generalizations of the conditional quantum mutual information of a tripartite state on $ABC$ (with $C$ being the conditioning system), which were shown to…
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…
Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…
We study the Renyi entropy in the finite temperature crossover regime of a Hubbard chain using quantum Monte Carlo. The ground state entropy has characteristic features such as a logarithmic divergence with block size and $2\kF$…
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…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…
Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…
In recent years, the Renyi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Renyi entropy is studied. A compact general formula is presented for the lower…
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…