# Negative Probability and Bell's Theorem

1. Feb 18, 2015

### Jilang

and was trying to find out more about how a negative probability might be interpreted. I came across this and wondered if anyone could shed more light on it.

"Let us consider the situation when an attentive person A with the high knowledge of English writes some text T. We may ask what the probability is for the word “texxt” or “wrod” to appear in his text T. Conventional probability theory gives 0 as the answer. However, we all know that there are usually misprints. So, due to such a misprint this word may appear but then it would be corrected. In terms of extended probability, a negative value (say, -0.1) of the probability for the word “texxt” to appear in his text T means that this word may appear due to a misprint but then it’ll be corrected and will not be present in the text T."

—Mark Burgin, Burgin, Mark (2010). "Interpretations of Negative Probabilities". http://arxiv.org/abs/1008.1287
[Mentor's note - edited to fix a link that was broken, probably by the forum software]

Is the "misprint' here referring to the uncertainty principle in some way?
Thanks.

Last edited by a moderator: Feb 18, 2015
2. Feb 19, 2015

### mathman

Highly unlikely. Uncertainty principle comes from quantum theory. Negative probability is a mathematical construction (which has no validity in conventional probability theory).

3. Feb 19, 2015

### Jilang

I was quite taken with this, but am not sure sure if I am following it correctly. If there is zero probability of finding a particle with a certain observable, but the uncertainty principle would have increased the probability, would the original probability have to have been negative to start with?

4. Feb 19, 2015

### atyy

5. Feb 19, 2015

### atyy

http://arxiv.org/abs/1409.5170
Wigner function negativity and contextuality in quantum computation on rebits
Nicolas Delfosse, Jacob Bian, Philippe Guerin and Robert Raussendorf

Another paper on negative probabilities:

http://arxiv.org/abs/1210.6870
Negative Probabilities, Fine's Theorem and Linear Positivity
J.J.Halliwell, J.M.Yearsley
http://dx.doi.org/10.1103/PhysRevA.87.022114

This paper discusses whether negativity is needed for a Bell inequality violation:

http://arxiv.org/abs/0710.5549v2
Negativity and contextuality are equivalent notions of nonclassicality
Robert W. Spekkens
http://dx.doi.org/10.1103/PhysRevLett.101.020401

Last edited: Feb 19, 2015
6. Feb 19, 2015