Informationally restricted correlations: a general framework for classical and quantum systems

We introduce new methods and tools to study and characterise classical and quantum correlations emerging from prepare-and-measure experiments with informationally restricted communication. We consider the most general kind of informationally restricted correlations, namely the ones formed when the sender is allowed to prepare statistical mixtures of mixed states, showing that contrary to what happens in Bell nonlocality, mixed states can outperform pure ones. We then leverage these tools to derive device-independent witnesses of the information content of quantum communication, witnesses for different quantum information resources, and demonstrate that these methods can be used to develop a new avenue for semi-device independent random number generators.

[1]  Armin Tavakoli,et al.  Experimental quantum multiparty communication protocols , 2016, npj Quantum Information.

[2]  W. Hager,et al.  and s , 2019, Shallow Water Hydraulics.

[3]  A. Acín,et al.  A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations , 2008, 0803.4290.

[4]  Mohamed Bourennane,et al.  Experimental device-independent tests of classical and quantum dimensions , 2011, Nature Physics.

[5]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[6]  Monique Laurent,et al.  Lower Bounds on Matrix Factorization Ranks via Noncommutative Polynomial Optimization , 2017, Found. Comput. Math..

[7]  崔久榮.  20 , 1978, The Murder of Marion Miley.

[8]  Danna Zhou,et al.  d. , 1840, Microbial pathogenesis.

[9]  Igor Klep,et al.  The tracial moment problem and trace-optimization of polynomials , 2013, Math. Program..

[10]  E. Woodhead,et al.  Correlations in Entanglement-Assisted Prepare-and-Measure Scenarios , 2021, PRX Quantum.

[11]  Erik Woodhead,et al.  Semi-device-independent framework based on natural physical assumptions , 2016, 1612.06828.

[12]  John Watrous,et al.  The Theory of Quantum Information , 2018 .

[13]  Igor Klep,et al.  Constrained trace-optimization of polynomials in freely noncommuting variables , 2016, J. Glob. Optim..

[14]  Andris Ambainis,et al.  Dense quantum coding and a lower bound for 1-way quantum automata , 1998, STOC '99.

[15]  Gerhard Reinelt,et al.  PANDA: a software for polyhedral transformations , 2015, EURO J. Comput. Optim..

[16]  N. Gisin,et al.  Informationally restricted quantum correlations , 2019, Quantum.

[17]  Stefano Pironio,et al.  Convergent Relaxations of Polynomial Optimization Problems with Noncommuting Variables , 2009, SIAM J. Optim..