Gibbs States and the Consistency of Local Density Matrices
| dc.creator | Liu, Yi-Kai | |
| dc.date | 2006-03-02 | |
| dc.date.accessioned | 2026-07-07T07:07:56Z | |
| dc.date.available | 2026-07-07T07:07:56Z | |
| dc.description | Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes some subset of the qubits. We say that rho_1,...,rho_m are "consistent" if there exists a global state sigma (on all n qubits) whose reduced density matrices match rho_1,...,rho_m. We prove the following result: if rho_1,...,rho_m are consistent with some state sigma > 0, then they are also consistent with a state sigma' of the form sigma' = (1/Z) exp(M_1+...+M_m), where each M_i is a Hermitian matrix acting on the same qubits as rho_i, and Z is a normalizing factor. (This is known as a Gibbs state.) Actually, we show a more general result, on the consistency of a set of expectation values <T_1>,...,<T_r>, where the observables T_1,...,T_r need not commute. This result was previously proved by Jaynes (1957) in the context of the maximum-entropy principle; here we provide a somewhat different proof, using properties of the partition function. | |
| dc.description | 5 pages, 1 figure; presented as a poster at SQuInT 2006 | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0603012 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0603012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110576 | |
| dc.subject | Quantum Physics | |
| dc.title | Gibbs States and the Consistency of Local Density Matrices | |
| dc.type | text |