Quantum coherence as asymmetry from complex weak values
- URL: http://arxiv.org/abs/2309.09157v1
- Date: Sun, 17 Sep 2023 04:53:18 GMT
- Title: Quantum coherence as asymmetry from complex weak values
- Authors: Agung Budiyono, Mohammad K. Agusta, Bagus E. B. Nurhandoko and
Hermawan K. Dipojono
- Abstract summary: We show that the average absolute imaginary part of the weak value of the generator of a translation group can be used to quantify the coherence as asymmetry relative to the translation group.
We argue that the quantifier of coherence so defined, called TC (translationally-covariant) w-coherence, can be obtained experimentally using a hybrid quantum-classical circuit.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum coherence as an asymmetry relative to a translation group generated
by a Hermitian operator, is a necessary resource for the quantum parameter
estimation. On the other hand, the sensitivity of the parameter estimation is
known to be related to the imaginary part of the weak value of the Hermitian
operator generating the unitary imprinting of the parameter being estimated.
This naturally suggests a question if one can use the imaginary part of the
weak value to characterize the coherence as asymmetry. In this work, we show
that the average absolute imaginary part of the weak value of the generator of
the translation group, maximized over all possible projective measurement
bases, can be used to quantify the coherence as asymmetry relative to the
translation group, satisfying certain desirable requirements. We argue that the
quantifier of coherence so defined, called TC (translationally-covariant)
w-coherence, can be obtained experimentally using a hybrid quantum-classical
circuit via the estimation of weak value combined with a classical optimization
procedure. We obtain upper bounds of the TC w-coherence in terms of the quantum
standard deviation, quantum Fisher information, and the imaginary part of the
Kirkwood-Dirac quasiprobability. We further obtain a lower bound and derive a
relation between the TC w-coherences relative to two generators of translation
group taking a form analogous to the Kennard-Weyl-Robertson uncertainty
relation.
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