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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

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Optimal work extraction from quantum batteries based on the expected utility hypothesis.

Gianluca Francica¹, Luca Dell'Anna¹

¹Dipartimento di Fisica e Astronomia e Sezione INFN, Università di Padova, 35131 Padova, Italy.

Physical Review. E

|May 17, 2024

Summary

This study explores optimal work extraction in quantum systems for risk-averse agents. It reveals that risk non-neutral agents use specific unitary transformations, dependent on their risk aversion, for efficient work extraction.

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Area of Science:

Quantum Thermodynamics
Quantum Information Theory
Statistical Mechanics

Background:

Work extraction is crucial in quantum thermodynamics, with ergotropy representing the maximum achievable work.
Traditional models assume risk-neutral agents, optimizing average work extraction.
Risk-averse agents, however, are influenced by work fluctuations and follow the expected utility hypothesis.

Purpose of the Study:

To investigate optimal work extraction strategies for risk non-neutral agents in quantum finite systems.
To analyze how an agent's risk aversion influences the work extraction process.
To examine work extraction from both incoherent and coherent initial quantum states.

Main Methods:

Maximizing the average utility function over all possible unitary cycles for risk non-neutral agents.
Focusing on initial states that are incoherent with respect to the energy basis.
Utilizing probability and quasiprobability distributions of work to model outcomes.

Main Results:

Optimal work extraction for incoherent states is achieved via incoherent unitary transformations (permutations of the energy basis).
The specific unitary transformation depends on the agent's degree of risk aversion.
Work extraction from ensembles of quantum batteries and the impact of initial coherence were also examined.

Conclusions:

Risk non-neutrality significantly alters optimal work extraction strategies in quantum systems.
Incoherent unitary transformations are key for risk-averse work extraction from incoherent states.
The framework provides insights into quantum thermodynamics for agents with varying risk preferences.