Set Of Free States Research Articles

An introductory review on resource theories of generalized nonclassical light

Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols that optimize its usefulness in a given application in areas ranging from quantum information to computation. Moreover, the resource theories have transmuted radical quantum phenomena like coherence, nonclassicality and entanglement from being just intriguing to being helpful in executing realistic thoughts. A general quantum resource theoretical framework relies on the method of categorization of all possible quantum states into two sets, namely, the free set and the resource set. Associated with the set of free states there is a number of free quantum operations emerging from the natural constraints attributed to the corresponding physical system. Then, the task of quantum resource theory is to discover possible aspects arising from the restricted set of operations as resources. Along with the rapid growth of various resource theories corresponding to standard harmonic oscillator quantum optical states, significant advancement has been expedited along the same direction for generalized quantum optical states. Generalized quantum optical framework strives to bring in several prosperous contemporary ideas including nonlinearity, -symmetric non-Hermitian theories, q-deformed bosonic systems, etc., to accomplish similar but elevated objectives of the standard quantum optics and information theories. In this article, we review the developments of nonclassical resource theories of different generalized quantum optical states and their usefulness in the context of quantum information theories.

Simple bounds for one-shot pure-state distillation in general resource theories

We present bounds for distilling many copies of a pure state from an arbitrary initial state in a general quantum resource theory. Our bounds apply to operations that are able to generate no more than a $\ensuremath{\delta}$ amount of resource, where $\ensuremath{\delta}\ensuremath{\ge}0$ is a given parameter. To maximize applicability of our upper bound, we assume little structure on the set of free states under consideration besides a weak form of superadditivity of the function ${G}_{\mathrm{min}}(\ensuremath{\rho})$, which measures the overlap between $\ensuremath{\rho}$ and the set of free states. Our bounds are given in terms of this function and the robustness of resource. Known results in coherence and entanglement theory are reproduced in this more general framework.

Gaussian quantum resource theories

We develop a general framework to assess capabilities and limitations of the Gaussian toolbox in continuous variable quantum information theory. Our framework allows us to characterize the structure and properties of quantum resource theories specialized to Gaussian states and Gaussian operations, establishing rigorous methods for their description and yielding a unified approach to their quantification. We show in particular that, under a few intuitive and physically motivated assumptions on the set of free states, no Gaussian quantum resource can be distilled with free Gaussian operations, even when an unlimited supply of the resource state is available. This places fundamental constraints on state manipulations in all such Gaussian resource theories. We discuss in particular the applications to quantum entanglement, where we extend previously known results by showing that Gaussian entanglement cannot be distilled even with Gaussian operations preserving the positivity of the partial transpose, as well as to other Gaussian resources such as steering and optical nonclassicality. A comprehensive semidefinite programming representation of all these resources is explicitly provided.

Optimization-free measures of quantum resources

A closed expression is derived for the amount of resource present in a quantum state as quantified by a distance measure based on the Tsallis relative entropy introduced recently [H. Zhao and C.-s. Yu, Sci. Rep. 8, 299 (2018)], for any resource theory whose set of free states is described by the image of a unital resource-destroying map. By applying it to the resource theory of coherence it is demonstrated that the correct definition of a projective coarse-grained measurement needs to be modified in order for it to be correctly interpreted as a measurement which provides less information about a system's true state than the one obtained from a finer-grained measurement.