A geometric interpretation for the $A$ fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the $A$ fidelity are studied by the numerical method. An alternative generalization of the $A$ fidelity, which has the same geometric picture, to an $N$ -state quantum system is also discussed.A geometric interpretation for the $A$ fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the $A$ fidelity are studied by the numerical method. An alternative generalization of the $A$ fidelity, which has the same geometric picture, to an $N$-state quantum system is also discussed.

arXiv:0809.1786Physical Review ADec 29, 200819 citations

A Geometric Interpretation of Quantum Mechanics

Nicole Bryant

Jul 24, 20260 citations

Geometric Interpretation of Sensitivity to Structured Uncertainties in Spintronic Networks

Sean P. O’Neil, EDMOND A. JONCKHEERE, Sophie Shermer

We present a geometric model of the differential sensitivity of the fidelity error for state transfer in a spintronic network based on the relationship between a set of matrix operators. We show an explicit dependence of the differential sensitivity on the fidelity (error), and we further demonstrate that this dependence does not require a trade-off between the fidelity and sensitivity. We prove that for closed systems, ideal performance in the sense of perfect state transfer is both necessary and sufficient for optimal robustness in terms of vanishing sensitivity. We demonstrate the utility of this geometric interpretation of the sensitivity by applying the model to explain the sensitivity versus fidelity error data in two examples.We present a geometric model of the differential sensitivity of the fidelity error for state transfer in a spintronic network based on the relationship between a set of matrix operators. We show an explicit dependence of the differential sensitivity on the fidelity (error), and we further demonstrate that this dependence does not require a trade-off between the fidelity and sensitivity. We prove that for closed systems, ideal performance in the sense of perfect state transfer is both necessary and sufficient for optimal robustness in terms of vanishing sensitivity. We demonstrate the utility of this geometric interpretation of the sensitivity by applying the model to explain the sensitivity versus fidelity error data in two examples.

arXiv:2501.13209IEEE Control Systems LettersJan 1, 20250 citations

A Geometric view of quantum mechanics

J. Anandan

Jan 1, 19892 citations

Alternative fidelity measure between two states of an N -state quantum system

Jing‐Ling Chen, Libin Fu, Abraham Albert Ungar +1 more

An alternative fidelity measure between two states of a qunit, an N-state quantum system, is proposed. It has a hyperbolic geometric interpretation, and it reduces to the Bures fidelity in the special case when $N=2.$ An alternative fidelity measure between two states of a qunit, an N-state quantum system, is proposed. It has a hyperbolic geometric interpretation, and it reduces to the Bures fidelity in the special case when $N=2.$

Physical Review AMay 8, 200260 citations

A geometric interpretation for the

A

fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the

A

fidelity are studied by the numerical method. An alternative generalization of the

A

fidelity, which has the same geometric picture, to an

N

-state quantum system is also discussed.

N=2.