Universal tradeoff relations between resource cost and irreversibility of channels: General-resource Wigner-Araki-Yanase theorems and beyond

TL;DR

This paper establishes a universal tradeoff between resource costs and irreversibility in quantum processes, applicable across various resource theories, and extends fundamental theorems like the Wigner-Araki-Yanase theorem to broader contexts.

Contribution

It introduces a universal cost-irreversibility tradeoff law for quantum channels applicable to multiple resource theories, extending key quantum measurement and resource limitations.

Findings

Lower irreversibility requires higher resource cost.

Universal relation between energetic cost and irreversibility for all channels.

Extension of the Wigner-Araki-Yanase theorem to general resource theories.

Abstract

Quantum technologies offer exceptional -- sometimes almost magical -- speed and performance, yet every quantum process costs physical resources. Designing next-generation quantum devices, therefore, depends on solving the following question: which resources, and in what amount, are required to implement a desired quantum process? Casting the problem in the language of quantum resource theories, we prove a universal cost-irreversibility tradeoff: the lower the irreversibility of a quantum process, the greater the required resource cost for its realization. The trade-off law holds for a broad range of resources -- energy, magic, asymmetry, coherence, athermality, and others -- yielding lower bounds on resource cost of any quantum channel. Its broad scope positions this result as a foundation for deriving the following key results: (1) we show a universal relation between the energetic cost and the irreversibility for arbitrary channels, encompassing the energy-error tradeoff for any measurement or unitary gate; (2) we extend the energy-error tradeoff to free energy and work costs; (3) we extend the Wigner-Araki-Yanase theorem, which is the universal limitation on measurements under conservation laws, to a wide class of resource theories: the probability of failure in distinguishing resourceful states via a measurement is inversely proportional to its resource cost; (4) we prove that infinitely many resource-non-increasing operations in fact require an infinite implementation cost. These findings reveal a universal relationship between quantumness and irreversibility, providing a first step toward a general theory that explains when -- and how -- quantumness can suppress irreversibility.