Quantum advantage by relational queries about physically realizable equivalence classes

Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive elementary cases is effectively partitioned into equivalence classes pertinent to the respective query. In the second part of the paper, we review recent progress in theoretical certifications (relative to the assumptions made) of quantum value indeterminacy as a means to build quantum oracles for randomness.

[1]  P. Dirac.  Principles of Quantum Mechanics , 1982 .

[2]  A. Gleason.  Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[3]  N. Mermin.  Quantum Computer Science: An Introduction , 2007 .

[4]  K. Svozil.  Quantum information in base n defined by state partitions , 2002, quant-ph/0205031.

[5]  N. David Mermin,et al.  What's Wrong with this Pillow? , 1989 .

[6]  F. London,et al.  La théorie de l'observation en mécanique quantique , 1939 .

[7]  J. Clauser.  Early History of Bell’s Theorem , 2002 .

[8]  Ehud Hrushovski,et al.  Generalizations of Kochen and Specker's theorem and the effectiveness of Gleason's theorem , 2003 .

[9]  Josef Tkadlec,et al.  On the solution of trivalent decision problems by quantum state identification , 2007, Natural Computing.

[10]  M. I. Dyakonov.  When shall we have a quantum computer , 2018 .

[11]  N. Mermin.  Quantum Computer Science , 2007 .

[12]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[13]  R. Feynman.  The Character of Physical Law , 1965 .

[14]  Michel Dyakonov.  When will we have a quantum computer , 2018 .

[15]  Mikhail I. Dyakonov,et al.  State of the Art and Prospects for Quantum Computing , 2013 .

[16]  K. Życzkowski,et al.  Geometry of Quantum States , 2007 .

[17]  Karl Svozil,et al.  Physical (A)Causality: Determinism, Randomness and Uncaused Events , 2018 .

[18]  Jack Copeland,et al.  Intelligent machinery , 2017, The Turing Guide.

[19]  P. Martin-Löf.  On the Notion of Randomness , 1970 .

[20]  M. Sipser,et al.  Limit on the Speed of Quantum Computation in Determining Parity , 1998, quant-ph/9802045.

[21]  K. Svozil.  Characterization of Quantum Computable Decision Problems by State Discrimination , 2005, quant-ph/0505129.

[22]  Berthold-Georg Englert,et al.  On quantum theory , 2013, 1308.5290.

[23]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[24]  Cristian S. Calude,et al.  On the Unpredictability of Individual Quantum Measurement Outcomes , 2014, Fields of Logic and Computation II.

[25]  I. Pitowsky.  Infinite and finite Gleason’s theorems and the logic of indeterminacy , 1998 .

[26]  K. Bray,et al.  Putting a stop to surface ignition , 1990 .

[27]  Cristian S. Calude,et al.  Experimentally probing the algorithmic randomness and incomputability of quantum randomness , 2018, Physica Scripta.

[28]  N. David Mermin,et al.  What's Wrong with these Equations? , 1989 .

[29]  Karl Svozil.  Quantum information via state partitions and the context translation principle , 2003 .

[30]  Cristian S. Calude,et al.  Kochen-Specker Theorem Revisited and Strong Incomputability of Quantum Randomness , 2012 .

[31]  E. Schrödinger.  Die gegenwärtige Situation in der Quantenmechanik , 2005, Naturwissenschaften.

[32]  Cristian S. Calude,et al.  Value-indefinite observables are almost everywhere , 2013, 1309.7188.

[33]  K. Wiesner.  The careless use of language in quantum information , 2017 .

[34]  Karl Svozil,et al.  Quantum Hocus Pocus , 2016, 1605.08569.

[35]  Cristian S. Calude,et al.  Experimental Evidence of Quantum Randomness Incomputability , 2010, ArXiv.

[36]  N David Mermin.  Making better sense of quantum mechanics. , 2019, Reports on progress in physics. Physical Society.

[37]  N. David Mermin,et al.  Could Feynman Have Said This , 2004 .

[38]  Scott Aaronson,et al.  Quantum Computing since Democritus , 2013 .

[39]  W. Myrvold.  Statistical mechanics and thermodynamics: A Maxwellian view , 2011 .

[40]  Asher Peres,et al.  Quantum Theory Needs No ‘Interpretation’ , 2000 .

[41]  K. Svozil,et al.  Finding a state among a complete set of orthogonal states , 2002 .

[42]  Jeffrey A. Barrett,et al.  The Everett interpretation of quantum mechanics : collected works 1955-1980 with commentary , 2012 .

[43]  Cristian S. Calude,et al.  A variant of the Kochen-Specker theorem localising value indefiniteness , 2015, 1503.01985.

[44]  Alexia Auffèves,et al.  Extracontextuality and extravalence in quantum mechanics , 2018, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[45]  Karl Svozil,et al.  New Forms of Quantum Value Indefiniteness Suggest That Incompatible Views on Contexts Are Epistemic , 2018, Entropy.