Universal tradeoff relations between resource cost and irreversibility of channels: General-resource Wigner-Araki-Yanase theorems and beyond
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909714135121920 |
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| author | Tajima, Hiroyasu Yamaguchi, Koji Takagi, Ryuji Kuramochi, Yui |
| author_facet | Tajima, Hiroyasu Yamaguchi, Koji Takagi, Ryuji Kuramochi, Yui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal tradeoff relations between resource cost and irreversibility of channels: General-resource Wigner-Araki-Yanase theorems and beyond Tajima, Hiroyasu Yamaguchi, Koji Takagi, Ryuji Kuramochi, Yui Quantum Physics Statistical Mechanics High Energy Physics - Theory 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. |
| title | Universal tradeoff relations between resource cost and irreversibility of channels: General-resource Wigner-Araki-Yanase theorems and beyond |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.23760 |