Information-based approach towards a unified resource theory

Abstract

Resource theories play an important role in quantum information theory, as they identify resourceful states and channels that are potentially useful for the accomplishment of tasks that would be otherwise unreachable. The elementary structure of such theories, which is based on the definition of free states and free operations, successfully accommodates different nonclassical aspects, such as quantum coherence and entanglement, but it is still not clear whether and how far such formal framework can be extended. In this work, by taking information as the most primitive quantum resource and defining resource-destroying operations, we develop a unifying approach that proves able to encompass several nonclassical aspects, including the newly developed concepts of quantum irreality and realism-based nonlocality.

Quantum realism: axiomatization and quantification

“…Inspired by a significant amount of theoretical and experimental works regarding the emergence of classicality from the quantum substratum [19,[22][23][24][25][26][27][28][29][30][31][32][33], here we propose an axiomatization for the concept of quantum realism. This notion is different from classical reality in a very fundamental manner, namely, non-commuting observables cannot be simultaneous elements of reality in general (Axiom 4).…”

“…Second, it would be useful, mainly for operational purposes, to have a picture of whether "metrics" other than the entropic ones, as for instance, norm-based quantifiers, can be used as sensible reality monotones. Finally, with regard to resource theories, although some evidences have been put forward suggesting that the A-irreality, I A (ρ) = ln d A − R A (ρ), can be viewed as a quantum resource [33], it would be interesting to have at hand a concrete information task wherein this concept configures a clear advantage in relation to contexts involving the A-reality state Φ A (ρ).…”

“…Incidentally, quantum realism cannot be thought of as a quantum resource because reality abounds for free in the classical regime. On the other hand, quantum realism is complementary to quantum irrealism (as quantified by irreality, which is believed to be a quantum resource [33]). With this inversion which may be identified with the dogma according to which all the systems exist and have well defined physical properties at every instant of time regardless the presence or action of observers (brain-endowed systems).…”

“…It becomes clear now the duality between irreality-a quantum resource per se [33]-and reality, which can thus be viewed as the amount of quantum resource that is destroyed when an observable is measured. Now we show that the quantifier (39) does satisfy Definition 2, which characterizes it as a reality measure.…”

“…The criterion of realism envisaged in this approach, henceforth referred to as BA's realism, does not imply full classical reality, since situations are shown to exist where the z-component of spin is an element of reality whereas the x-component is not. Many developments followed from this framework, from a novel notion of nonlocality [27][28][29] to foundational aspects of quantum theory [19,30] and their proof-of-principle [31,32] to the realization that irreality is a quantum resource [33].…”