Device-independent certification of degeneracy-breaking measurements
- URL: http://arxiv.org/abs/2311.04497v1
- Date: Wed, 8 Nov 2023 07:10:39 GMT
- Title: Device-independent certification of degeneracy-breaking measurements
- Authors: Prabuddha Roy, Shyam Sundar Mahato, Sumit Mukherjee, and A. K. Pan
- Abstract summary: We demonstrate the device-independent certification of degeneracy-breaking measurement based on the sequential Bell test.
We use an elegant sum-of-squares approach that powers such certification of degeneracy-breaking measurements.
- Score: 2.06242362470764
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: In a device-independent Bell test, the devices are considered to be black
boxes and the dimension of the system remains unspecified. The dichotomic
observables involved in such a Bell test can be degenerate and one may invoke a
suitable measurement scheme to lift the degeneracy. However, the standard Bell
test cannot account for whether or up to what extent the degeneracy is lifted,
as the effect of lifting the degeneracy can only be reflected in the
post-measurement states, which the standard Bell tests do not certify. In this
work, we demonstrate the device-independent certification of
degeneracy-breaking measurement based on the sequential Bell test by multiple
observers who perform degeneracy-breaking unsharp measurements characterized by
positive-operator-valued measures (POVMs) - the noisy variants of projectors.
The optimal quantum violation of Clauser-Horne-Shimony-Holt inequality by
multiple sequential observers eventually enables us to certify up to what
extent the degeneracy has been lifted. In particular, our protocol certifies
the upper bound on the number of POVMs used for performing such measurements
along with the entangled state and measurement observables. We use an elegant
sum-of-squares approach that powers such certification of degeneracy-breaking
measurements.
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