Complementary Information Principle and Universal Uncertainty - PowerPoint PPT Presentation

Complementary Information Principle and Universal Uncertainty Regions (arXiv:1908.07694) Yunlong Xiao 1 , Kun Fang 2 and Gilad Gour 1 1. University of Calgary 2. DAMTP, University of Cambridge Presented at AQIS 2019, KIAS Seoul

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<latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> A Bit of History Physical scenario of preparational UR M N Γ ρ Γ ρ p q A short history [see e.g. Coles-Berta-Tomamichel-Wehner’17, RMP] • 1927, Heisenberg: (heuristic idea) impossible to prepare a state such that its outcome probability distributions from the position and moment observables are both sharp. • 1927, Kennard/ 1928, Weyl: ∆ ( Q ) ∆ ( P ) ≥ ~ / 2 1983, Deutsch: • H ( M ) + H ( N ) ≥ const. • 1988, Maassen-Uffink: H α ( M ) + H β ( N ) ≥ − log c, 1 / α + 1 / β = 2 2010, Berta-Christandl-Colbeck-Renes-Renner: H ( M | B ) + H ( N | B ) ≥ − log c + H ( A | B ) • 2011, Partovi/ 2013, Friedland-Gheorghiu-Gour: p ⌦ q � ω •

A Plethora of Applications Determine Nonlocality e.g. Oppenheim, J. and Wehner, S., 2010. The uncertainty principle determines the nonlocality of quantum mechanics. Science , 330 (6007), pp.1072-1074. Witness Entanglement e.g. Hofmann, H.F. and Takeuchi, S., 2003. Violation of local uncertainty relations as a signature of entanglement. Physical Review A , 68 (3), p.032103. Detect Non-Markovianity Uncertainty e.g. Maity, A.G., Bhattacharya, S. and Maujmdar, A.S., 2019. Detecting non- Relation Markovianity via uncertainty relations. arXiv preprint arXiv:1901.02372 . Secure Quantum Cryptography/QKD e.g. Ng, N.H.Y., Berta, M. and Wehner, S., 2012. Min-entropy uncertainty relation for finite-size cryptography. Physical Review A , 86 (4), p.042315. Certify Quantum Randomness e.g. Miller, C.A. and Shi, Y., 2016. Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices. Journal of the ACM (JACM) , 63 (4), p.33.