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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.
In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance T 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.
When a Dicke states has been prepared in an experiment, it is important to verify that the state has been prepared with a good quality. Apart from obtaining the fidelity, a usual goal is to show that the quantum state was highly entangled. If for a quantum state the fidelity with respect to W-states
The purity of a normalized quantum state satisfies , [1] where is the dimension of the Hilbert space upon which the state is defined. The upper bound is obtained by tr ( ρ ) = 1 {\displaystyle \operatorname {tr} (\rho )=1\,} and tr ( ρ 2 ) ≤ tr ( ρ ) {\displaystyle \operatorname {tr} (\rho ^{2})\leq \operatorname {tr} (\rho ...
Assuming that | is a ground state of a parameter-dependent non-degenerate Hamiltonian (), four times the quantum Fisher information of this state is called fidelity susceptibility, and denoted [13]
A quantum state for an imperfectly isolated system will generally evolve to be entangled with the quantum state for the environment. Consequently, even if the system's initial state is pure, the state at a later time, found by taking the partial trace of the joint system-environment state, will be mixed. This phenomenon of entanglement produced ...
As superconducting quantum computing approaches larger scale devices, researchers face difficulties in qubit coherence, scalable calibration software, efficient determination of fidelity of quantum states across an entire chip, and qubit and gate fidelity. [16]
Similarly, quantum states consist of sets of dynamical variables that evolve under equations of motion. However, the values derived from quantum states are complex numbers, quantized, limited by uncertainty relations, [1]: 159 and only provide a probability distribution for the outcomes for a system. These constraints alter the nature of ...