Quantum Resource Theory
The core of a resource theory is built upon two main system-dependent requirements for the resources and allowed operations; namely, (i) the existence of a set of states that are free and those not in the set are expensive; and (ii) the allowed operations are those that map the set of free states to itself. Various resource theories have been developed in the past decade. The most notable example is the resource theory of entanglement, where the set of free states corresponds to the collection of separable states and the allowed free operations are the local quantum operations and classical communication (LOCC). These two classes of states and operations have attracted standalone interests besides resource theory. Under this resource framework, one can then ask the amount of valuable resource (cf. quantum entanglement) possessed by an entangled state relative to the set of free states (cf. separable states). This question motivates the scenario of injecting noise locally to the system in order to destroy the quantum entanglement, i.e., the randomness cost. A complete characterization of this question has remained open; though, gapped upper and lower bounds have been provided in the asymptotic i.i.d. setting. It is worthwhile to mention that investigation of a variant of the above setting, where the local noise is used to destroy the total correlation in an entangled state, relates the minimal randomness cost to the quantum mutual information . This seminal result gives the first operational meaning to this entropic quantity and advances significantly our understanding of entanglement theory. Being able to answer the optimal randomness cost to bring entangled states to separable states thus bears equivalent significance, if not more important, since the existence of entanglement is believed to make quantum systems superior to their classical counterparts and the amount of entanglement is generally linked to its information-processing power. Likewise, this crucial question of the amount of valuable resource possessed by a state relative to its free resource is then adhesive to every resource theory, be it quantum coherence, thermodynamics, etc.
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