Frame-dependent coherence of a quantum state
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911180320145408 |
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| author | Cotfas, Nicolae |
| author_facet | Cotfas, Nicolae |
| contents | The tight frames can be regarded as a particular case of POVMs (positive operator-valued measures describing generalized measurements), namely the case when all the operators are rank-one. Each orthonormal basis is a tight frame, and every tight frame, after the embedding into a higher-dimensional space, is the orthogonal projection of an orthonormal basis. There exist several POVM-based definitions of coherence, and they are well-investigated. Our aim is to identify properties specific to the particular case of tight frames, and to look for some applications. All the POVM-based definitions use a Naimark extension. The frame-dependent coherence can be regarded as a particular case of POVM-based coherence, but it can be defined directly, without to use a Naimark extension. Its definition is a direct generalization of the basis-dependent $\ell_1$-norm of coherence, and it offers a more accurate description because we can use a frame containing several orthogonal bases. A frame-invariant definition of coherence for qubits and multi-qubit systems is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04178 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frame-dependent coherence of a quantum state Cotfas, Nicolae Quantum Physics The tight frames can be regarded as a particular case of POVMs (positive operator-valued measures describing generalized measurements), namely the case when all the operators are rank-one. Each orthonormal basis is a tight frame, and every tight frame, after the embedding into a higher-dimensional space, is the orthogonal projection of an orthonormal basis. There exist several POVM-based definitions of coherence, and they are well-investigated. Our aim is to identify properties specific to the particular case of tight frames, and to look for some applications. All the POVM-based definitions use a Naimark extension. The frame-dependent coherence can be regarded as a particular case of POVM-based coherence, but it can be defined directly, without to use a Naimark extension. Its definition is a direct generalization of the basis-dependent $\ell_1$-norm of coherence, and it offers a more accurate description because we can use a frame containing several orthogonal bases. A frame-invariant definition of coherence for qubits and multi-qubit systems is presented. |
| title | Frame-dependent coherence of a quantum state |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.04178 |