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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".
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 ...
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
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.
Fidelity (%) Qubits (physical) Release date Quantum volume Alpine Quantum Technologies PINE System [2] Trapped ion: 24 [3] June 7, 2021: 128 [4] Atom Computing Phoenix Neutral atoms in optical lattices: 100 [5] August 10, 2021: Atom Computing N/A Neutral atoms in optical lattices: 35×35 lattice (with 45 vacancies) < 99.5 (2 qubits) [6] 1180 [7 ...
Though perfect quantum cloning is not possible, it is possible to perform imperfect cloning, where the copies have a non-unit (i.e. non-perfect) fidelity. The possibility of approximate quantum copying was first addressed by Buzek and Hillery, [1] and theoretical bounds were derived on the fidelity of cloned quantum states. [2]
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]