dorsal/arxiv
View SchemaA mathematical foundation of quantum information and quantum computer -on quantum mutual entropy and entanglement-
| Authors | Masanori Ohya |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9808051 |
| URL | https://arxiv.org/abs/quant-ph/9808051 |
Abstract
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical input and quantum output. In 1983, the autho r defined the fully quantum mechanical mutual entropy by means of the relati ve entropy of Umegaki, and it has been used to compute the capacity of quant um channel for quantum communication process; quantum input-quantum output. Recently, a correlated state in quantum syatems, so-called quantum entangled state or quantum entanglement, are used to study quntum information, in part icular, quantum computation, quantum teleportation, quantum cryptography. In this paper, we mainly discuss three things below: (1) We point out the di fference between the capacity of quantum channel and that of classical-quant um-classical channel. (2) So far the entangled state is merely defined as a non-separable state, we give a wider definition of the entangled state and c lassify the entangled states into three categories. (3) The quantum mutual e ntropy for an entangled state is discussed. The above (2) and (3) are a join t work with Belavkin.
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"abstract": "The study of mutual entropy (information) and capacity in classica l system\nwas extensively done after Shannon by several authors like Kolmogor ov and\nGelfand. In quantum systems, there have been several definitions of t he mutual\nentropy for classical input and quantum output. In 1983, the autho r defined\nthe fully quantum mechanical mutual entropy by means of the relati ve entropy\nof Umegaki, and it has been used to compute the capacity of quant um channel\nfor quantum communication process; quantum input-quantum output.\n Recently, a correlated state in quantum syatems, so-called quantum entangled\nstate or quantum entanglement, are used to study quntum information, in part\nicular, quantum computation, quantum teleportation, quantum cryptography.\n In this paper, we mainly discuss three things below: (1) We point out the di\nfference between the capacity of quantum channel and that of classical-quant\num-classical channel. (2) So far the entangled state is merely defined as a\nnon-separable state, we give a wider definition of the entangled state and c\nlassify the entangled states into three categories. (3) The quantum mutual e\nntropy for an entangled state is discussed. The above (2) and (3) are a join t\nwork with Belavkin.",
"arxiv_id": "quant-ph/9808051",
"authors": [
"Masanori Ohya"
],
"categories": [
"quant-ph"
],
"title": "A mathematical foundation of quantum information and quantum computer -on quantum mutual entropy and entanglement-",
"url": "https://arxiv.org/abs/quant-ph/9808051"
},
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