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The fidelity between two quantum states and , expressed as density matrices, is commonly defined as: [1] [2] (,) = ().The square roots in this expression are well-defined because both and are positive semidefinite matrices, and the square root of a positive semidefinite matrix is defined via the spectral theorem.
From the beginning of organised motor sport events, in the early 1900s, until the late 1960s, before commercial sponsorship liveries came into common use, vehicles competing in Formula One, sports car racing, touring car racing and other international auto racing competitions customarily painted their cars in standardised racing colours that indicated the nation of origin of the car or driver.
In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions.
A density operator that is a rank-1 projection is known as a pure quantum state, and all quantum states that are not pure are designated mixed. Pure states are also known as wavefunctions . Assigning a pure state to a quantum system implies certainty about the outcome of some measurement on that system (i.e., P ( x ) = 1 {\displaystyle P(x)=1 ...
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 ...
The IPR basically takes the full information about a quantum system (the wave function; for a -dimensional Hilbert space one would have to store values, the components of the wave function) and compresses it into one single number that then only contains some information about the localization properties of the state.
Here are a few examples of books that use the now-adopted definition of F: Geometry of Quantum States: An Introduction to Quantum Entanglement (Bengtsson), Quantum Information: An Overview (Jaeger), Exploring the Quantum (Haroche), Quantum Information (Barnett), A Guide to Experiments in Quantum Optics (Bachor), Quantum Optics (Walls & Milburn ...
For mixed states, the concurrence can be defined by convex roof extension. [ 3 ] For the tangle, there is monogamy of entanglement , [ 9 ] [ 10 ] that is, the tangle of a qubit with the rest of the system cannot ever exceed the sum of the tangles of qubit pairs which it is part of.