![]() ![]() Given any pair of quantum states, they can be classified as: (i) IO-comparable, when one state can be transformed into the other by means of IO, (ii) IO-equivalent, when both states can be transformed into the other, and (iii) IO-incomparable, when neither state can be transformed into the other.Īnother way to capture operational aspects of coherence is by means of coherence quantifiers. This preorder is useful for studying coherence transformations and classifying the set of quantum states according to its coherence resource power. The resource-theoretic formulation allows us to introduce a preorder between quantum states induced by the incoherent operations: one state is more or equally coherent than other if the former can be converted into the later by means of incoherent operations. In this work, we follow the definition of an incoherent operation (IO) introduced in 3, which has the property that coherence can not be created from an incoherent state, not even in a probabilistic way. Regarding the free operations of the theory, there is no single definition and each proposal leads to a different resource theory for coherence, see e.g. The rest of the states are resources and they are called coherent states. The free states of the theory, called incoherent states, are quantum states with diagonal density matrix in the incoherent basis. Since coherence is a basis-dependent notion, these three elements are defined in terms of a fixed basis, called incoherent basis. Furthermore, within the paradigm of quantum resource theories 2, quantum coherence is considered as a quantum resource that can be converted, consumed and quantified 3, 4.Īs any resource theory, the resource theory of coherence is built from three basic concepts: free states, resources and free operations. It has practical relevance in numerous fields of quantum physics, particularly in quantum information processing 1. 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.Quantum coherence, which is a consequence of the superposition principle, is one of the fundamental aspects of the quantum 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. This seminal result gives the first operational meaning to this entropic quantity and advances significantly our understanding of entanglement theory. 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. A complete characterization of this question has remained open though, gapped upper and lower bounds have been provided in the asymptotic i.i.d. This question motivates the scenario of injecting noise locally to the system in order to destroy the quantum entanglement, i.e., the randomness cost. quantum entanglement) possessed by an entangled state relative to the set of free states (cf. Under this resource framework, one can then ask the amount of valuable resource (cf. These two classes of states and operations have attracted standalone interests besides resource theory. 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). Various resource theories have been developed in the past decade. ![]() 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.
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