dorsal/arxiv
View SchemaPartial transposition on bi-partite system
| Authors | Y. -J. Han, X. J. Ren, Y. C. Wu, G. -C. Guo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609091 |
| URL | https://arxiv.org/abs/quant-ph/0609091 |
Abstract
Many of the properties of the partial transposition are not clear so far. Here the number of the negative eigenvalues of K(T)(the partial transposition of K) is considered carefully when K is a two-partite state. There are strong evidences to show that the number of negative eigenvalues of K(T) is N(N-1)/2 at most when K is a state in Hilbert space N*N. For the special case, 2*2 system(two qubits), we use this result to give a partial proof of the conjecture sqrt(K(T))(T)>=0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of K(T) or the negative entropy of K.
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"abstract": "Many of the properties of the partial transposition are not clear so far.\nHere the number of the negative eigenvalues of K(T)(the partial transposition\nof K) is considered carefully when K is a two-partite state. There are strong\nevidences to show that the number of negative eigenvalues of K(T) is N(N-1)/2\nat most when K is a state in Hilbert space N*N. For the special case, 2*2\nsystem(two qubits), we use this result to give a partial proof of the\nconjecture sqrt(K(T))(T)\u003e=0. We find that this conjecture is strongly connected\nwith the entanglement of the state corresponding to the negative eigenvalue of\nK(T) or the negative entropy of K.",
"arxiv_id": "quant-ph/0609091",
"authors": [
"Y. -J. Han",
"X. J. Ren",
"Y. C. Wu",
"G. -C. Guo"
],
"categories": [
"quant-ph"
],
"title": "Partial transposition on bi-partite system",
"url": "https://arxiv.org/abs/quant-ph/0609091"
},
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"source": {
"execution_id": "3fc39f08-4d1d-4293-90a6-0c8646d40f53",
"id": "arXiv Dataset IDs",
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"variant": "snapshot-2026-03-01",
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