Universal limitations on implementing resourceful unitary evolutions

Abstract

We derive a trade-off relation between the accuracy of implementing a desired unitary evolution using a restricted set of free unitaries and the size of the assisting system, in terms of the resource generating/losing capacity of the target unitary. In particular, this relation implies that, for any theory equipped with a resource measure satisfying lenient conditions, any resource changing unitary cannot be perfectly implemented by a free unitary applied to a system and an environment if the environment has finite dimensions. Our results are applicable to a wide class of resources including energy, asymmetry, coherence, entanglement, and magic, imposing ultimate limitations inherent in such important physical settings, as well as providing insights into operational restrictions in general resource theories.

8+2 pages

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Cited by in corpus (13)

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• One-Shot Manipulation of Dynamical Quantum Resources
• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
• Autonomous Quantum Devices: When Are They Realizable without Additional Thermodynamic Costs?
• Universal limitation of quantum information recovery: symmetry versus coherence
• Wigner-Araki-Yanase theorem for continuous and unbounded conserved observables
• Robustness of controlled Hamiltonian approaches to unitary quantum gates
• Energy requirement for implementing unitary gates on energy-unbounded systems
• The Hadamard gate cannot be replaced by a resource state in universal quantum computation
• A quantum reference frame size-accuracy trade-off for quantum channels