DOI: 10.14704/nq.2013.11.4.691

Probability Constraints on the Classical/Quantum Divide

Subhash Kak


This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being different (Pn). Given three events, Ps/Pn for the classical case where there are no 3-way coincidences is one-half whereas for the maximally entangled quantum state it is one-third. For non-maximally entangled objects kak.png we find that so long as r < 5.83, we can separate them from classical objects using a probability test. For maximally entangled particles (r = 1), we propose that the value of 5/12 be used for Ps/Pn to separate classical and quantum states when no other information is available and measurements are noisy.

NeuroQuantology | December 2013 | Volume 11 | Issue 4 | Page 600-606


information; Bell inequality; quantum theory; entanglement; probability constraints

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Ball P. The dawn of quantum biology. Nature 2011; 474: 272-274.

Bell J. On the Einstein Podolsky Rosen paradox. Physics 1964; 1 (3): 195–200.

Boole G. On the theory of probabilities. Philos Trans R Soc London 1862; 152: 225-252.

Briggs JS and Eisfeld A. Equivalence of quantum and classical coherence in electronic energy transfer. Phys Rev E 2011; 83: 051911–051914.

Brunner N et al., Bell nonlocality. 2013. arXiv:1303.2849.

Christensen BG et al., Detection-loophole-free test of quantum nonlocality and applications. 2013. arXiv:1306.5772.

Collini E et al., Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 2010; 463: 644–648.

De Raedt H, Hess K, Michielsen K. Extended Boole-Bell inequalities applicable to quantum theory. J Comp Theor Nanosci 2011; 8: 1011 – 1039.

Ferry DK. Probing Bell’s inequality with classical systems. Fluctuation and Noise Letters 2010; 9: 395-402.

Freeman W and Vitiello G. Nonlinear brain dynamics as macroscopic manifestation of underlying many-body dynamics. Physics of Life Reviews 2006; 3: 93-118.

Hameroff S and Penrose R. Conscious events as orchestrated space-time selections. NeuroQuantology 2003; 1: 10-35.

Kak S. Quantum neural computing. In Advances in Imaging and Electron Physics, vol. 94, P. Hawkes (editor). Academic Press, 259-313, 1995.

Kak S. The three languages of the brain: quantum, reorganizational, and associative. In Learning as Self-Organization, K. Pribram and J. King (editors). Lawrence Erlbaum Associates, Mahwah, NJ, 185-219, 1996.

Kak S. Active agents, intelligence, and quantum computing. Information Sciences 2000; 128: 1-17.

Kak S. Quantum information and entropy. International Journal of Theoretical Physics 2007; 46, 860-876.

Kak S. Another look at quantum neural computing. 2009. arXiv:0908.3148.

Kak S. The problem of testing a quantum gate. Infocommunications Journal 2012; 4 (4): 18-22.

Kak S. The universe, quantum physics, and consciousness. Journal of Cosmology 2009; 3: 500-510.

Kak S. Biological memories and agents as quantum collectives. NeuroQuantology 2013; 11(3): 391-398.

Khrennikov AY. Ubiquitous Quantum Structure: From Psychology to Finance. Springer, Berlin, 2010.

Lambert N et al., Quantum biology. Nature Physics 2013; 9:10–18.

Maccone A. A simple proof of Bell’s inequality. 2012. arXiv:1212.5214.

Miller WH. Perspective: Quantum or classical coherence? J Chem Phys 2012; 136: 210901.

‘t Hooft G. Entangled quantum states in a local deterministic theory. 2009. arXiv:0908.3408..

Vervoort L. Bell’s theorem: Two neglected solutions. Foundations of Physics 2013; 43:769–791.

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The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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