Quantum Lunch: Ultimate data hiding in quantum mechanics and beyond – University of Copenhagen

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Quantum Lunch: Ultimate data hiding in quantum mechanics and beyond

Ludovico Lami from Universitat Autònoma de Barcelona

Title: Ultimate data hiding in quantum mechanics and beyond 

Data hiding in quantum mechanics was originally discovered in [1] (see also [2]). Since we are interested in studying the intrinsic limits of this phenomenon, I will start by introducing a more fundamental framework known as general probabilistic theories (GPTs) [3], which is an abstract way to generalise quantum probability rules as to encompass only the most basic physical requirements. Within the realm of GPTs, we will define what we mean by data hiding using the language of norms discussed in [4]. By making an unexpected connection with Grothendieck’s theory of tensor norms, we will study the ultimate limits of this non-classical phenomenon as arising from only basic physical constraints. Quantum mechanics is found to have a data hiding efficiency of the order of the square root of the maximal one. In other words, Nature is non-classical, but not as non-classical as it could have been.

[1] B. M. Terhal, D. P. DiVincenzo, and D. W. Leung, Hiding bits in Bell states, Phys. Rev. Lett. 86, 5807 (2001); arXiv:quant- ph/0011042. 

[2] Chapter 4 of Eggeling’s PhD thesis http://d-nb.info/967787947/34.

[3] H. Barnum, J. Barrett, M. Leifer, and A. Wilce, Teleportation in general probabilistic theories, Proceedings of Symposia in Applied Mathematics 71, 25-48 (2012); arXiv:0805.3553 (2008). 

[4] W. Matthews, S. Wehner, and A. Winter, Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding, Comm. Math. Phys. 291(3), 813-843 (2009); arXiv:0810.2327.