dorsal/arxiv
View SchemaA New Relation between post and pre-optimal measurement states
| Authors | Chirag Dhara, N. D. Hari Dass |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406169 |
| URL | https://arxiv.org/abs/quant-ph/0406169 |
| DOI | 10.1103/PhysRevA.72.024102 |
| Journal | Phys.Rev. A72 024102(2005) |
Abstract
When an optimal measurement is made on a qubit and what we call an Unbiased Mixture of the resulting ensembles is taken, then the post measurement density matrix is shown to be related to the pre-measurement density matrix through a simple and linear relation. It is shown that such a relation holds only when the measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is also shown explicitly that non-orthogonal measurements fail to give such a linear relation no matter how the ensembles are mixed. The result has been proved to be true for arbitrary quantum mechanical systems of finite dimensional Hilbert spaces. The result is true irrespective of whether the initial state is pure or mixed.
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"abstract": "When an optimal measurement is made on a qubit and what we call an Unbiased\nMixture of the resulting ensembles is taken, then the post measurement density\nmatrix is shown to be related to the pre-measurement density matrix through a\nsimple and linear relation. It is shown that such a relation holds only when\nthe measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is\nalso shown explicitly that non-orthogonal measurements fail to give such a\nlinear relation no matter how the ensembles are mixed. The result has been\nproved to be true for arbitrary quantum mechanical systems of finite\ndimensional Hilbert spaces. The result is true irrespective of whether the\ninitial state is pure or mixed.",
"arxiv_id": "quant-ph/0406169",
"authors": [
"Chirag Dhara",
"N. D. Hari Dass"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.024102",
"journal_ref": "Phys.Rev. A72 024102(2005)",
"title": "A New Relation between post and pre-optimal measurement states",
"url": "https://arxiv.org/abs/quant-ph/0406169"
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