Riemannian metric on the space of mixed states of a quantum system
In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures)[1] or Helstrom metric (named after Carl W. Helstrom)[2] defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric[3] when restricted to the pure states alone.
^Bures, Donald (1969). "An extension of Kakutani's theorem on infinite product measures to the tensor product of semifinite *-algebras" (PDF). Transactions of the American Mathematical Society. 135. American Mathematical Society (AMS): 199. doi:10.1090/s0002-9947-1969-0236719-2. ISSN 0002-9947.
^Helstrom, C.W. (1967). "Minimum mean-squared error of estimates in quantum statistics". Physics Letters A. 25 (2). Elsevier BV: 101–102. Bibcode:1967PhLA...25..101H. doi:10.1016/0375-9601(67)90366-0. ISSN 0375-9601.
^Facchi, Paolo; Kulkarni, Ravi; Man'ko, V.I.; Marmo, Giuseppe; Sudarshan, E.C.G.; Ventriglia, Franco (2010). "Classical and quantum Fisher information in the geometrical formulation of quantum mechanics". Physics Letters A. 374 (48): 4801–4803. arXiv:1009.5219. Bibcode:2010PhLA..374.4801F. doi:10.1016/j.physleta.2010.10.005. ISSN 0375-9601. S2CID 55558124.
the area of quantum information geometry, the Buresmetric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal...
space, it becomes the Fubini–Study metric; when written in terms of mixed states, it is the quantum Buresmetric. Considered purely as a matrix, it is...
{\boldsymbol {\theta }}} . This definition is identical to four times the Buresmetric, up to singular points where the rank of the density matrix changes (those...
the second term (involving the trace) is precisely the (unnormalised) Buresmetric between C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} . This...
the other. The fidelity is not a metric on the space of density matrices, but it can be used to define the Buresmetric on this space. The fidelity between...
})} , where D B {\displaystyle D_{B}} is the Bures distance between the starting and ending states. The Bures distance is geodesic, giving the shortest possible...
television series, part of the Marvel Cinematic Universe Helstrom metric (or Buresmetric), in quantum mechanics and mathematics, defining an infinitesimal...
could fit on any given bar. BUR plates were offered only in American pounds; the metric system was never used for any BUR branded product. Bars and Collars...
9 km for the "Bur" surface-to-surface missiles. It had a rate of fire of 4-5 rounds/min for the "Rubin", and 8-10 rounds/min for the "Bur". Both munitions...
accuracy of measuring the circumference. Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations, the exceptions being...
laboratory for the United States. Southard had previously sponsored a bill for metric conversion of the United States. President Theodore Roosevelt appointed...
i=1,\ldots ,n} . This distance is compatible with Fisher metric. It is also related to Bures distance and fidelity between quantum states as for two diagonal...
stiffness-over-density-cubed metric is at best a starting point for analysis. For example, most wood species score better than most metals on this metric, but many metals...
Airport, owned by the city of Ontario, CA; serves the Inland Empire. (IATA: BUR, ICAO: KBUR) Hollywood Burbank Airport, jointly owned by the cities of Burbank...
in 2008 were India (4 million metric tons), Bangladesh (2.16 million metric tons), and the Sudan (1.47 million metric tons). India slaughters 41% of...
following mass shootings". The Washington Post. Retrieved October 3, 2021. Bures, Brendan (February 21, 2020). "Trump administration doubles down on anti-marijuana...
areas. The handling capacity of the centre is anticipated to exceed 300,000 metric tonnes of product throughput per annum. The cold storage facility at Dubai...
1985 until 1995, professor at Institut des Hautes Études Scientifiques at Bures-sur-Yvette in France, at the Institute for Advanced Study in Princeton,...
for the building of the new vessel, varying in size from 4,800 to 7,500 metric tons (4,700 to 7,400 long tons) and with armaments and speed in various...
on February 7, 1997. Distances and other measurements are displayed in metric units. Warning signs are usually placed 150 metres before the area they're...
States) MMscfd – million standard cubic feet per day MMTPA – millions of metric tonnes per annum MMstb – million stock barrels MNP – merge and playback...
poor and the downtrodden. As Cartier puts it, Grothendieck came to find Bures-sur-Yvette as "une cage dorée" ("a gilded cage"). While Grothendieck was...
reach 100 kg or more. A few have fragments that total even more than one metric ton. The six largest falls are listed below and five (except the 2013 Chelyabinsk...
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