dorsal/arxiv
View SchemaAn expectation value expansion of Hermitian operators in a discrete Hilbert space
| Authors | Roberth Asplund, Gunnar Bjork, Mohamed Bourenanne |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011037 |
| URL | https://arxiv.org/abs/quant-ph/0011037 |
| DOI | 10.1088/1464-4266/3/3/314 |
Abstract
We discuss a real-valued expansion of any Hermitian operator defined in a Hilbert space of finite dimension N, where N is a prime number, or an integer power of a prime. The expansion has a direct interpretation in terms of the operator expectation values for a set of complementary bases. The expansion can be said to be the complement of the discrete Wigner function. We expect the expansion to be of use in quantum information applications since qubits typically are represented by a discrete, and finite-dimensional physical system of dimension N=2^p, where p is the number of qubits involved. As a particular example we use the expansion to prove that an intermediate measurement basis (a Breidbart basis) cannot be found if the Hilbert space dimension is 3 or 4.
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"abstract": "We discuss a real-valued expansion of any Hermitian operator defined in a\nHilbert space of finite dimension N, where N is a prime number, or an integer\npower of a prime. The expansion has a direct interpretation in terms of the\noperator expectation values for a set of complementary bases. The expansion can\nbe said to be the complement of the discrete Wigner function.\n We expect the expansion to be of use in quantum information applications\nsince qubits typically are represented by a discrete, and finite-dimensional\nphysical system of dimension N=2^p, where p is the number of qubits involved.\nAs a particular example we use the expansion to prove that an intermediate\nmeasurement basis (a Breidbart basis) cannot be found if the Hilbert space\ndimension is 3 or 4.",
"arxiv_id": "quant-ph/0011037",
"authors": [
"Roberth Asplund",
"Gunnar Bjork",
"Mohamed Bourenanne"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/3/3/314",
"title": "An expectation value expansion of Hermitian operators in a discrete Hilbert space",
"url": "https://arxiv.org/abs/quant-ph/0011037"
},
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