Related papers: Relative Entropy and Catalytic Relative Majorizati…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…
We propose an approach to the study of quantum resource manipulation based on the basic observation that quantum channels which preserve certain sets of states are contractive with respect to the base norms induced by those sets. We forgo…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
We show that the generalization of the relative entropy of a resource from states to channels is not unique, and there are at least six such generalizations. We then show that two of these generalizations are asymptotically continuous,…
Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined…
A central question since the beginning of quantum information science is how two distant parties can convert one entangled state into another. It has been conjectured that such conversions could be executed reversibly in an asymptotic…
I show that whenever a system undergoes a reproducible macroscopic process the mutual distinguishability of macrostates, as measured by their relative entropy, diminishes. This extends the second law which regards only ordinary entropies,…
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…
Quantum resource theories (QRTs) provide a unified theoretical framework for understanding inherent quantum-mechanical properties that serve as resources in quantum information processing, but resources motivated by physics may possess…
Randomness is a defining element of mixing processes in nature and an essential ingredient to many protocols in quantum information. In this work, we investigate how much randomness is required to transform a given quantum state into…
In 2016, A. Winter et al.(Physical Review Letters 116 (12) (2016) 120404) provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocol in asymptotic…
Quantum entanglement is the quantum information processing resource. Thus it is of importance to understand how much of entanglement particular quantum states have, and what kinds of laws entanglement and also transformation between…
We generalize the theory of catalytic quantum randomness to delocalized and dynamical settings. First, we expand the resource theory of randomness (RTR) by calculating the amount of entropy catalytically extractable from a correlated or…
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification…
An important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under…
Entanglement is a key quantum resource in various quantum protocols, with a rich set of laws governing its manipulation. In this context, catalysis refers to the possibility of an auxiliary state that enables a previously forbidden…
The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different…
The difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking. We develop a general approach to this…
We study the relative entropy of highly excited quantum states. First, we sample states from the Wishart ensemble and develop a large-N diagrammatic technique for the relative entropy. The solution is exactly expressed in terms of…