Superfidelity

'''Superfidelity''' is a measure of similarity between density operators. It is defined as G(\rho,\sigma) = \mathrm{tr}\rho\sigma + \sqrt{1-\mathrm{tr}(\rho^2)}\sqrt{1-\mathrm{tr}(\sigma^2)}, where \sigma and \rho are density matrices. Superfidelity was introduced inmiszczak09sub as an upper bound for fidelity. == Properties == Super-fidelity has also properties which make it useful for quantifying distance between quantum states. In particular we have: * Bounds: 0 \le G(\rho_1,\rho_2) \le 1. * Symmetry: \; G(\rho_1,\rho_2)= G(\rho_2,\rho_1). * Unitary invariance: for any unitary operator \ U, we have \; G(\rho_1,\rho_2)=G(U\rho_1U^{\dagger},U\rho_2U^{\dagger}). * Concavity: : G(\rho_1,\alpha \rho_2 + (1-\alpha)\rho_3) \geq \alpha G(\rho_1,\rho_2) + (1-\alpha) G(\rho_1,\rho_3) for any \rho_1,\rho_2,\rho_3\in\Omega_N and \alpha \in [0,1]. * Supermultiplicativity: for \rho_1,\rho_2,\rho_3,\rho_4 \in \Omega_N we have : G(\rho_1 \otimes \rho_2, \rho_3 \otimes \rho_4) \geq G(\rho_1,\rho_3) G(\rho_2,\rho_4). == See also == * Fidelity * Trace distance * Trace norm == References == Category:Handbook of Quantum Information Category:Mathematical Structure Category:Linear Algebra

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Monday, October 26, 2015 - 17:56