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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.
More explicitly, this is the quantity | |, with the maximization performed with respect to all possible POVMs {}. To understand why this maximum equals the trace distance between the states, note that there is a unique decomposition ρ − σ = P − Q {\displaystyle \rho -\sigma =P-Q} with P , Q ≥ 0 {\displaystyle P,Q\geq 0} positive ...
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.
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One of the first cloning machines, a 1 to 2 UQC machine, was proposed in 1996 by Buzek and Hillery. [10] 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.
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The same approach has been used in chemical photography to capture an extremely wide dynamic range: A three-layer film with each underlying layer at one hundredth (10 −2) the sensitivity of the next higher one has, for example, been used to record nuclear-weapons tests. [56] Consumer-grade image file formats sometimes restrict dynamic range. [57]
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