Operational interpretation and estimation of quantum trace-norm
asymmetry based on weak value measurement and some bounds
- URL: http://arxiv.org/abs/2309.09159v1
- Date: Sun, 17 Sep 2023 05:12:13 GMT
- Title: Operational interpretation and estimation of quantum trace-norm
asymmetry based on weak value measurement and some bounds
- Authors: Agung Budiyono
- Abstract summary: An important and geometrically intuitive measure of translational asymmetry of a state is given by the trace-norm asymmetry.
We show that the trace-norm asymmetry is equal to the average absolute imaginary part of the weak value of the generator of the translation group optimized over all possible orthonormal bases of the Hilbert space.
We then use the link between the trace-norm asymmetry and the nonreal weak value to derive the relation between the trace-norm asymmetry with other basic concepts in quantum statistics.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The asymmetry of a quantum state relative to a translational group is a
central concept in many areas of quantum science and technology. An important
and geometrically intuitive measure of translational asymmetry of a state is
given by the trace-norm asymmetry, which is defined as the trace norm of the
commutator between the state and the generator of the translation group. While
trace-norm asymmetry satisfies all the requirements for a bonafide measure of
translational asymmetry of a state within the quantum resource theoretical
framework, its meaning in terms of laboratory operations is still missing.
Here, we first show that the trace-norm asymmetry is equal to the average
absolute imaginary part of the weak value of the generator of the translation
group optimized over all possible orthonormal bases of the Hilbert space.
Hence, it can be estimated via the measurement of weak value combined with a
classical optimization in the fashion of quantum variational circuit which may
be implemented using the near-term quantum hardware. We then use the link
between the trace-norm asymmetry and the nonreal weak value to derive the
relation between the trace-norm asymmetry with other basic concepts in quantum
statistics. We further obtain trade-off relations for the trace-norm asymmetry
and quantum Fisher information, having analogous forms to the
Kennard-Weyl-Robertson uncertainty relation.
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