Hilbert-Schmidt speed as an efficient tool in quantum metrology

• URL: http://arxiv.org/abs/2009.06050v1
• Date: Sun, 13 Sep 2020 17:52:25 GMT
• Title: Hilbert-Schmidt speed as an efficient tool in quantum metrology
• Authors: Hossein Rangani Jahromi and Rosario Lo Franco
• Abstract summary: We exploit the Hilbert-Schmidt speed (HSS) as a powerful tool for quantum phase estimation in a $n$-qubit system. Our results provide strong evidence for contractivity of the HSS under completely positive and trace preserving maps in high-dimensional systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate how the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, can be exploited as a powerful and easily computable tool for quantum phase estimation in a $n$-qubit system. We find that, when both the HSS and quantum Fisher information (QFI) are computed with respect to the phase parameter encoded into the initial state of the $n$-qubit register, the zeros of the HSS dynamics are essentially the same as those of the QFI dynamics. Moreover, the positivity (negativity) of the time-derivative of the HSS exactly coincides with the positivity (negativity) of the time-derivative of the QFI. Our results also provide strong evidence for contractivity of the HSS under completely positive and trace preserving maps in high-dimensional systems, as predicted in previous studies.

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