Related papers: On Variational Expressions for Quantum Relative En…
Relative entropy (divergence) of Bregman type recently proposed by T. D. Frank and Jan Naudts is considered and its quantum counterpart is used to calculate purity of the Werner state in nonextensive formalism. It has been observed that two…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
In this paper it was proved that the quantum relative entropy $D(\sigma \| \rho)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $\rho$,…
We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties,…
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 introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of…
In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback-Leibler Divergence) between measures mu and P on the space of continuous functions from time 0 to T. The underlying measure P is…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
Quantum generalizations of R\'enyi's entropies are a useful tool to describe a variety of operational tasks in quantum information processing. Two families of such generalizations turn out to be particularly useful: the Petz quantum R\'enyi…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the…
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…
In the absence of a reference frame for transformations associated with a group G, any quantum state that is non-invariant under the action of G may serve as a token of the missing reference frame. We here introduce a novel measure of the…
In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…
We describe a quantum algorithm to estimate the $\alpha$-Renyi entropy of an unknown density matrix $\rho\in\mathcal{C}^{d\times d}$ for $\alpha\neq 1$ by combining the recent technique of quantum singular value transformations with the…
Simply and reliably detecting and quantifying entanglement outside laboratory conditions will be essential for future quantum information technologies. Here we address this issue by proposing a method for generating expressions which can…
R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…