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Fidelity is symmetric in its arguments, i.e. F (ρ,σ) = F (σ,ρ). Note that this is not obvious from the original definition. F (ρ,σ) lies in [0,1], by the Cauchy–Schwarz inequality. F (ρ,σ) = 1 if and only if ρ = σ, since Ψ ρ = Ψ σ implies ρ = σ. So we can see that fidelity behaves almost like a metric.
In quantum mechanics, each physical system is associated with a Hilbert space, each element of which represents a possible state of the physical system.The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable".
On the Bloch sphere, pure states are represented by a point on the surface of the sphere, whereas mixed states are represented by an interior point.Thus, the purity of a state can be visualized as the degree to which the point is close to the surface of the sphere.
As the name implies, the machine produces two identical copies of a single input qubit with a fidelity of 5/6 when comparing only one output qubit, and global fidelity of 2/3 when comparing both qubits. This idea was expanded to more general cases such as an arbitrary number of inputs and copies, [11] as well as d-dimensional systems. [12]
Vinyl microgroove phonograph records typically yield 55-65 dB, though the first play of the higher-fidelity outer rings can achieve a dynamic range of 70 dB. [25] German magnetic tape in 1941 was reported to have had a dynamic range of 60 dB, [26] though modern-day restoration experts of such tapes note 45-50 dB as the observed dynamic range. [27]
We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information theory: the output of a channel at a given time depends only upon the corresponding input and not any previous ones.
This list contains quantum processors, also known as quantum processing units (QPUs).Some devices listed below have only been announced at press conferences so far, with no actual demonstrations or scientific publications characterizing the performance.
The D mesons were discovered in 1976 by the Mark I detector at the Stanford Linear Accelerator Center. [3]Since the D mesons are the lightest mesons containing a single charm quark (or antiquark), they must change the charm (anti)quark into an (anti)quark of another type to decay.