Joint measurability in nonequilibrium quantum thermodynamics

Abstract

In this Letter we investigate the concept of quantum work and its measurability from the viewpoint of quantum measurement theory. Very often, quantum work and fluctuation theorems are discussed in the framework of projective two-point measurement (TPM) schemes. According to a well known no-go theorem, there is no work observable which satisfies both (i) an average work condition and (ii) the TPM statistics for diagonal input states. Such projective measurements represent a restrictive class among all possible measurements. It is desirable, both from a theoretical and experimental point of view, to extend the scheme to the general case including suitably designed unsharp measurements. This shifts the focus to the question what information about work and its fluctuations one is able to extract from such generalized measurements. We show that the no-go theorem no longer holds if the observables in a TPM scheme are jointly measurable for any intermediate unitary evolution. We explicitly construct a model with unsharp energy measurements and derive bounds for the visibility that ensure joint measurability. In such an unsharp scenario a single work measurement apparatus can be constructed that allows us to determine the correct average work and to obtain free energy differences with the help of a Jarzynski equality.

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Cited by in corpus (11)

• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• Quasiprobabilities in quantum thermodynamics and many-body systems
• Work fluctuations and entanglement in quantum batteries
• Quantum measurements constrained by the third law of thermodynamics
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Energy conservation and fluctuation theorem are incompatible for quantum work
• Quantum work: Reconciling quantum mechanics and thermodynamics
• Thermodynamically free quantum measurements
• Naimark dilations of qubit POVMs and joint measurements
• Retrievability of information in quantum and realistic hidden variable theories
• Barycentric decomposition for quantum instruments