Density Hypercubes, Higher Order Interference and Hyper-decoherence: A Categorical Approach

In this work, we use the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes. By considering multi-slit experiments, we show that the theory displays higher-order interference of order up to fourth. We also show that the theory possesses hyperdecoherence maps, which can be used to recover quantum theory in the Karoubi envelope.

[1]  Rafael D. Sorkin.  Quantum Measure Theory and its Interpretation , 1995 .

[2]  Jiangfeng Du,et al.  Experimental test of Born's rule by inspecting third-order quantum interference on a single spin in solids , 2016, 1612.08563.

[3]  G. Niestegge.  Three-Slit Experiments and Quantum Nonlocality , 2011, 1104.0091.

[4]  John H. Selby,et al.  Deriving Grover's lower bound from simple physical principles , 2016, 1604.03118.

[5]  Bob Coecke.  Terminality Implies No-signalling ...and Much More Than That , 2016, New Generation Computing.

[7]  Dusko Pavlovic,et al.  A new description of orthogonal bases , 2008, Mathematical Structures in Computer Science.

[8]  G. D’Ariano,et al.  Probabilistic theories with purification , 2009, 0908.1583.

[9]  R. Laflamme,et al.  Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule , 2012, 1207.2321.

[10]  C. Ududec.  Perspectives on the Formalism of Quantum Theory , 2012 .

[11]  Stefano Gogioso,et al.  Categorical Probabilistic Theories , 2017, QPL.

[12]  R. Sorkin.  Quantum mechanics as quantum measure theory , 1994, gr-qc/9401003.

[13]  T. Paterek,et al.  Density cubes and higher-order interference theories , 2013, 1308.2822.

[14]  John H. Selby,et al.  Oracles and Query Lower Bounds in Generalised Probabilistic Theories , 2017, Foundations of Physics.

[15]  Ciarán M Lee,et al.  A no-go theorem for theories that decohere to quantum mechanics , 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  Aninda Sinha,et al.  On the superposition principle in interference experiments , 2014, Scientific Reports.

[17]  Giulio Chiribella,et al.  Microcanonical thermodynamics in general physical theories , 2016, 1608.04460.

[18]  Markus P. Mueller,et al.  Higher-order interference and single-system postulates characterizing quantum theory , 2014, 1403.4147.

[19]  J. Emerson,et al.  Three Slit Experiments and the Structure of Quantum Theory , 2009, 0909.4787.

[20]  Simon Perdrix,et al.  Environment and Classical Channels in Categorical Quantum Mechanics , 2010, CSL.

[21]  Howard Barnum,et al.  Thermodynamics and the structure of quantum theory , 2016, 1608.04461.

[22]  Howard Barnum,et al.  Ruling out Higher-Order Interference from Purity Principles , 2017, Entropy.

[23]  G. Weihs,et al.  Obtaining tight bounds on higher-order interferences with a 5-path interferometer , 2015, 1508.03253.

[24]  S. Gogioso.  Higher-order CPM Constructions , 2018, Electronic Proceedings in Theoretical Computer Science.

[25]  John H. Selby,et al.  Higher-Order Interference in Extensions of Quantum Theory , 2015, 1510.03860.

[26]  Giulio Chiribella,et al.  Entanglement as an axiomatic foundation for statistical mechanics , 2016, ArXiv.

[27]  K. Życzkowski.  Quartic quantum theory: an extension of the standard quantum mechanics , 2008, 0804.1247.

[28]  R. Laflamme,et al.  Ruling Out Multi-Order Interference in Quantum Mechanics , 2010, Science.

[29]  Raymond Lal,et al.  Causal Categories: Relativistically Interacting Processes , 2011, 1107.6019.

[30]  John H. Selby,et al.  Generalised phase kick-back: the structure of computational algorithms from physical principles , 2015, 1510.04699.