dorsal/arxiv
View SchemaQuantum thermodynamics with missing reference frames: Decompositions of free energy into non-increasing components
| Authors | Dominik Janzing |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511271 |
| URL | https://arxiv.org/abs/quant-ph/0511271 |
| DOI | 10.1007/s10955-006-9220-x |
Abstract
If an absolute reference frame with respect to time, position, or orientation is missing one can only implement quantum operations which are covariant with respect to the corresponding unitary symmetry group G. Extending observations of Vaccaro et al., I argue that the free energy of a quantum system with G-invariant Hamiltonian then splits up into the Holevo information of the orbit of the state under the action of G and the free energy of its orbit average. These two kinds of free energy cannot be converted into each other. The first component is subadditive and the second superadditive; in the limit of infinitely many copies only the usual free energy matters. Refined splittings of free energy into more than two independent (non-increasing) terms can be defined by averaging over probability measures on G that differ from the Haar measure. Even in the presence of a reference frame, these results provide lower bounds on the amount of free energy that is lost after applying a covariant channel. If the channel properly decreases one of these quantities, it decreases the free energy necessarily at least by the same amount, since it is unable to convert the different forms of free energies into each other.
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"abstract": "If an absolute reference frame with respect to time, position, or orientation\nis missing one can only implement quantum operations which are covariant with\nrespect to the corresponding unitary symmetry group G. Extending observations\nof Vaccaro et al., I argue that the free energy of a quantum system with\nG-invariant Hamiltonian then splits up into the Holevo information of the orbit\nof the state under the action of G and the free energy of its orbit average.\nThese two kinds of free energy cannot be converted into each other. The first\ncomponent is subadditive and the second superadditive; in the limit of\ninfinitely many copies only the usual free energy matters.\n Refined splittings of free energy into more than two independent\n(non-increasing) terms can be defined by averaging over probability measures on\nG that differ from the Haar measure.\n Even in the presence of a reference frame, these results provide lower bounds\non the amount of free energy that is lost after applying a covariant channel.\nIf the channel properly decreases one of these quantities, it decreases the\nfree energy necessarily at least by the same amount, since it is unable to\nconvert the different forms of free energies into each other.",
"arxiv_id": "quant-ph/0511271",
"authors": [
"Dominik Janzing"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10955-006-9220-x",
"title": "Quantum thermodynamics with missing reference frames: Decompositions of free energy into non-increasing components",
"url": "https://arxiv.org/abs/quant-ph/0511271"
},
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