Encraption Hypothesis: “The behavior of entangled particles can be explained by each particle having an internal PRNG. Sometimes two or more particles’ PRNG states sync up in such a way that they do the same (or opposite) things when observed.”

This explains some – but not all – of the behavior of entangled particles. It explains how when faraway labs measure entangled particles, they always see the same random outcome (or the opposite random outcome, depending on the kind of entanglement). But, in the lab, we see particles doing things that can’t be explained by this model: violating bell inequalities.

Bell inequalities confuse me, so I prefer to talk about “nonlocal games” which are closely related to Bell inequalities and much easier for cryptographers to understand.

Here’s the setup. There are two players, Alice and Bob, who you can imagine are separated by lightyears of distance so they cannot communicate. In between, there is a Referee who challenges Alice and Bob to a game. The referee generates two truly random bits X and Y and sends X in Alice’s direction and Y in Bob’s direction. Alice and Bob each send a bit back to the Referee, and their replies have to come back fast enough for the Referee to be convinced they haven’t communicated with each other in the meantime (since information can’t travel faster than light).

Pictorially: Alice Referee Bob

Let’s call the bit Alice sends back “A” and the bit bob sends back “B”. They win the game if X AND Y = A XOR B.

How often on average can Alice and Bob win the game? It turns out that if you model Alice and Bob as probabilistic Turing machines (which you can, under the Encraption Hypothesis), then the best possible strategy wins 75% of the time. You can prove this by considering all possible deterministic strategies and then seeing probabilistic strategy outcomes as averages of different deterministic strategy outcomes (https://cs.uwaterloo.ca/~watrous/CPSC519/LectureNotes/20.pdf).

In the real world, if Alice and Bob share entangled particles, then they can win with ~85% probability. This is better than what they could do if they were probabilistic Turing machines, so if the Referee sees them winning this frequently, then the Referee can conclude Alice and Bob are more than just probabilistic Turing machines, and that the Encraption Hypothesis is false.

If you already understand quantum mechanics math, you can read this to see how they achieve ~85% probability of winning: https://sergworks.wordpress.com/2016/10/26/chsh-game-in-detail/

I’ll try to give an intuition in English about what’s happening.

Suppose Alice and Bob each have a photon, and the two photons’ polarizations are entangled. Alice and Bob can choose to measure their respective photons’ polarizations at any angles. For example, one of them can ask their photon “Are you polarized vertically or horizontally?” or instead they could ask “Are you polarized at a 45° angle or a 135° angle?” No matter what angle the photon is actually polarized at, they’ll always measure it to be in one of the two possibilities in the question they ask, and after they ask the question, the photon’s polarization changes to the state consistent with the answer.

Because of the entanglement, if Alice and Bob both ask the same question, e.g. they both ask “Are you polarized vertically or horizontally?” then they will get the same (random) answer. If they ask opposite questions, then they both get independently random outcomes.

They can also ask questions at angles in between “horizontal vs. vertical” and “45° vs 135°”. The more aligned their questions are, the more likely they are to get the same outcome. The more misaligned their questions are, the more likely their outputs are to be random and uncorrelated.

So the trick to winning the game is this: They choose which question they’ll ask their photons based on their input from the Referee, and they do this in a special way so that:

1. If X AND Y = 1, then their questions will be more-misaligned and thus their answers will be closer to independently random, making it more likely that A XOR B = 1.

2. If X AND Y = 0, then their questions will be more-aligned and thus their answers will be more likely to agree, making it more likely that A XOR B = 0.

This works experimentally, so we have to accept one of three things:

1. The universe conspires to break the Referee’s random number generator so that X and Y aren’t actually random but are correlated in a way that let Alice and Bob win.

2. Alice and Bob are communicating somehow.

3. Alice and Bob can’t actually be thought of as two separate physical systems with their states independently described by probabilistic Turing machines.

(1) and (2) are called Bell test “loopholes” and scientists have been doing better and better experiments to rule them out. The latest in this series of experiments is https://thebigbelltest.org/ in which (1) would imply an insane conspiracy between the states of particles in the brains of people all around the world.

]]>I don’t suppose you could post a copy somewhere else, you know, a site that doesn’t block people at random? 🙂

]]>Come on, you broke it before.

Are you sure there isn’t some DNS-rebinding attacks still possible to printer down the hall ? 😉

I’m sure there are still lots of recurse DNS servers which don’t block internal IPs (and internal IPs are easier to get/guess now with WebRTC).

]]>What he pointed out was that a serious deep-packet-capable inspection machine was about the same price as most people’s primary router, so that selective collection was as expensive as capitalizing the ISP in the first place, and that the alternative was to (do a man-in-the middle attack and) spool everything off to a couple of large disks, round-robin.

That, of course, then made the ISP an attractive nuisance, the target of any smart cracker who wanted to collect credit-card numbers and data for blackmail, any security service on the planet, and any police officer on a fishing expedition that could get a specific warrant and then offer to filter it out of the general data.

In addition, it provided a real advantage to the monopoly telephone and cable-base ISPs, who could afford to dedicate a Sandvine box or two, and argue that anyone who can’t isn’t obeying the law. And, of course, shouldn’t be allowed to be in the business.

Thus far, it hasn’t happened in Canada. Well, at least as far as we know (;-))

I wonder what’s the situation in the US?

–dave

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