Yes / A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered
in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices
which resolve the identity, and makes them a `generalized basis', which is practically useful. The
dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses
Mobius transforms. There is non-independence and redundancy in these generalized bases, which is
quantifi ed with a Shannon type of entropy. Due to this redundancy, calculations based on generalized
bases, are sensitive to physical changes and robust in the presence of noise. For example, the
representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in
the coeffcients. Also in a physical system with ground state which changes abruptly at some value
of the coupling constant, the proposed methodology detects such changes, even when noise is added
to the parameters in the Hamiltonian of the system.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/12580 |
| Date | 23 June 2017 |
| Creators | Vourdas, Apostolos |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Article, Accepted Manuscript |
| Rights | © 2017 IOP Publishing Ltd. Reproduced in accordance with the publisher's self-archiving policy. |
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