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

• URL: http://arxiv.org/abs/2507.23760v1
• Date: Thu, 31 Jul 2025 17:48:14 GMT
• Title: Universal tradeoff relations between resource cost and irreversibility of channels: General-resource Wigner-Araki-Yanase theorems and beyond
• Authors: Hiroyasu Tajima, Koji Yamaguchi, Ryuji Takagi, Yui Kuramochi,
• Abstract summary: We show a universal relation between the energetic cost and the irreversibility for arbitrary channels.<n>We extend the energy-error tradeoff to free energy and work costs.<n>These findings reveal a universal relationship between quantumness and irreversibility.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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