Search results
Results from the WOW.Com Content Network
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.
The formula for this calculation is known as the Born rule. For example, a quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude. Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region ...
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Wavefunction: ψ, Ψ To solve from the Schrödinger equation: varies with situation and number of particles Wavefunction probability density: ρ = | | = m −3 [L] −3: Wavefunction probability current: j
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 ...
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.
The formula also holds without taking the real part , because the imaginary part leads to an antisymmetric contribution that disappears under the sum. Note that all eigenvalues λ k {\displaystyle \lambda _{k}} and eigenvectors | k {\displaystyle \vert k\rangle } of the density matrix potentially depend on the vector of parameters θ ...
In quantum mechanics, the Schrödinger equation describes how a system changes with time. It does this by relating changes in the state of the system to the energy in the system (given by an operator called the Hamiltonian).
In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state that has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator.