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An expectation value expansion of Hermitian operators in a discrete Hilbert space
KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.ORCID iD: 0000-0002-2082-9583
2001 (English)In: Journal of Optics B-Quantum and Semiclassical Optics, ISSN 1464-4266, E-ISSN 1741-3575, Vol. 3, no 3, 163-170 p.Article in journal (Refereed) Published
Abstract [en]

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 three or four.

Place, publisher, year, edition, pages
2001. Vol. 3, no 3, 163-170 p.
Keyword [en]
quantum cryptography, Hermitian operators, state reconstruction, Breidbart basis, stern-gerlach measurements, quantum-state tomography, wigner-function, spin-s, cryptography, ensembles, mechanics, systems, factorization, entanglement
URN: urn:nbn:se:kth:diva-20796ISI: 000169878000015OAI: diva2:339493
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Björk, Gunnar
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