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My favorite not-quite-probability distribution
Yunger Halpern, Nicole - UMD
Presentation on Thursday, Oct. 7, 2021, noon
Location: Virtual Seminars over Zoom Until Further Notice
Quasiprobability distributions resemble probability distributions but can
contain negative and imaginary values. Such distributions represent
quantum states as probability distributions over phase space represent
states in classical statistical mechanics. Many quasiprobabilities exist, the
most famous being the Wigner function. Among the least famous ranks the
Kirkwood-Dirac distribution, discovered during the early 1900s and then
forgotten. But the Kirkwood-Dirac distribution has been enjoying a
renaissance recently: Applications range from quantum chaos to
tomography, metrology, foundations, and thermodynamics. I will introduce
the Kirkwood-Dirac distribution and illustrate its usefulness: The
quasiprobability can be used to prove that operators’ noncommmutation—a
nonclassical phenomenon—underlies a protocol’s effectiveness in quantum
metrology. I aim to convince you that the Kirkwood-Dirac distribution is the
best little quasiprobability you’d never heard of.
References
1) Arvidsson-Shukur, NYH, Lepage, Lasek, Barnes, and Lloyd, Nat.
Comms. 11, 3775 (2020).
2) Arvidsson-Shukur, Drori-Chevalier, and NYH, J. Phys. A 54, 284001
(2021).
3) Lupu-Gladstein, Yilmaz, Arvidsson-Shukur, Brodutch, Pang, Steinberg,
and NYH (in prep).
4) NYH, Swingle, and Dressel, Phys. Rev. A 97, 042105 (2018).