Minimum time for the evolution to a nonorthogonal quantum state and upper bound of the geometric efficiency of quantum evolutions

• URL: http://arxiv.org/abs/2106.09378v2
• Date: Mon, 16 Aug 2021 08:43:06 GMT
• Title: Minimum time for the evolution to a nonorthogonal quantum state and upper bound of the geometric efficiency of quantum evolutions
• Authors: Carlo Cafaro, Paul M. Alsing
• Abstract summary: We present a proof of the minimum time for the quantum evolution between two arbitrary states. We discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a simple proof of the minimum time for the quantum evolution between two arbitrary states. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the efficiency inequality even when the system passes only through nonorthogonal quantum states.

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