The Age of Entanglement Untappable C^3?

[Jack Sarfatti]

Excerpts from:

"Can relativity be considered complete?

From Newtonian nonlocality to quantum nonlocality and beyond
http://arXiv:quant-ph/0512168 v1 20 Dec 2005

Nicolas Gisin
Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
(Dated: December 20, 2005)
We review the long history of nonlocality in physics with special
emphasis on the conceptual breakthroughs over the last few years. For
the first time it is possible to study "nonlocality without signaling"
from the outside, that is without all the quantum physics Hilbert space
artillery. We emphasize that physics has always given a nonlocal
description of Nature, except during a short 10 years gap. We note that
the very concept of "nonlocality without signaling" is totally foreign
to the

I. INTRODUCTION
100 years after Einstein's miraculous year and 70 years after the EPR
paper [1], I like to think that Einstein would have appreciated the
somewhat provocative title of this contribution. However, Einstein would
probably not have liked its conclusion. But who can doubt that
relativity is incomplete? and likewise that quantum mechanics is
incomplete! Indeed, these are two scientific theories and Science is
nowhere near its end (as a matter of fact, I do believe that there is no
end [2]). Well, actually, I am, of course, not writing for Einstein, but
for those readers interested in a (necessarily somewhat subjective)
account of the peaceful co-existence[3] between relativity and quantum
physics in the light of the conceptual and experimental progresses that
happened during the last ten years, set in the broad perspective of
physics and nonlocality since Newton [4].
II. NON-LOCALITY ACCORDING TO NEWTON
Isaac Newton, the great Newton of Universal Gravitation, was not
entirely happy with his theory. Indeed, he was well aware of an awkward
consequence of his theory: if a stone is moved on the moon, then our
weight, of all of us, here on earth, is immediately modified. What
troubled Newton so much was this immediate effect, i.e. the nonlocal
prediction of his theory. Let's read how Newton described it himself [5]:

'That Gravity should be innate, inherent and essential to Matter, so
that one Body may act upon another at a Distance thro a Vacuum, without
the mediation of anything else, by and through which their Action and
Force may be conveyed from one to another, is to me so great an
Absurdity, that I believe no Man who has in philosophical Matters a
competent Faculty of thinking, can ever fall into it. Gravity must be
caused by an Agent acting constantly according to certain Laws, but
whether this Agent be material or immaterial , I have left to the
Consideration of my Readers.'

It would have been hard for Newton to be more explicit in his rejection
of nonlocality! However, most physicists didn't pay much attention to
this aspect of Newtonian physics. By lack of alternative, physics
remained nonlocal until about 1915 when Einstein introduced the world to
General Relativity. But let's start ten years earlier, in 1905.
III. EINSTEIN, THE GREATEST MECHANICAL ENGINEER
In 1905 Einstein introduced three radically new theories or models in
physics. Special relativity of course, but more relevant to this section
are his descriptions of Brownian motion and of the photo-electric effect.
Indeed, both descriptions show Einstein's deep intuition about
mechanics. Brownian motion is explained as a complex series of
billiard-ball-like-collisions between a visible molecule-the particle
undergoing Brownian motion -and invisible smaller particles. The random
collisions of the latter explaining the erratic motion of the former.
Likewise, the photo-electric effect is given a mechanistic explanation.
Light beams contain little billiard-balls whose energy depends on the
color, i.e. wavelength, of the light. These light-billiard-balls (today
called photons and recognized as not at all billiard-ball-like) hit the
electrons on metallic surfaces and mechanically kick them out of the
metal, provided they have enough energy.

General relativity can also be seen as a mechanical description of
gravitation. When a stone is moved on the moon, a bunch of gravitons (in
modern terminology) fly off in all directions at a finite speed, the speed
of light."
Gisin has jumped too quick. You do not need to invoke gravitons, which
may not exist. Einstein's 1915 GR is a complete classical field theory
that does not need gravitons to explain what happens when you move a
stone. There is a deep conflict between gravity and quantum theory.
Gravity may well be an emergent macro-quantum theory i.e. an effective
low energy c-number theory without any spin 2 quanta at all. All the
quanta may be only spin 1 or spin 1/2 & spin 0. Maybe spin 3/2. Or, in any
case, the best we may be able to do is perturbation theory for spin 2
linear "gravitons" on a curved c-number space-time background.

"Hence, about a second later, the earth is informed and only then is our
weight affected. This is, I believe, the greatest achievement of
Einstein, the greatest mechanical engineer1of all times: Einstein turned
physics into
1My friends know well that in my mouth "engineer" has no negative
connotation, quite the opposite. For me, a physicist must be a good
theorist and a good engineer! Well, I warned you, dear reader, this is a
somewhat subjective article.

IV. QUANTUM MECHANICS IS NOT MECHANICAL
Only about ten years after general relativity came quantum mechanics.
This was quite an extraordinary revolution. Until then, greatly thanks
to Newton and Einstein's genius, Nature was seen as made out of many
little billiard-balls that mechanically bang into each other. Yet,
quantum mechanics is characterized by the very fact that it no longer
gives a mechanical description of Nature. The terminology quantum
mechanics is just a historical mistake, it should be called Quantum
Physics as it is a radically new sort of physical description of Nature.

But this new description let nonlocality back into Physics! And this was
unacceptable for Einstein."

And spontaneous broken symmetry of the physical vacuum with local
coherent generic Higgs fields but locality back into physics. Note that
it is the electroweak Higgs field that gives mass to leptons, quarks and
weakons. But it is the different Planck Higgs field that gives us
Einstein's curved space-time theory of gravity as a c-number Goldstone
phase field as distinct from a Higgs intensity field.

"It is remarkable and little noticed that since Newton, physics gave a
local description of Nature only during some 10 years, between about
1915 and 1925. All the rest of the time, it was nonlocal, though, with
quantum physics, in quite a different sense as with Newton gravitation.
Indeed, the latter implies the possibility of arbitrarily fast
signaling, while the former prohibits it."
However, post-quantum theories allow such signaling. Weinberg , Stapp
and Valentini gave examples. Weinberg's rejection was invalid because
he did not look at complex non-equilibrium systems.

V. NON-LOCALITY ACCORDING TO EINSTEIN
In 1935 two celebrated papers appeared in respectable journals, both
with famous authors, both stressing the unacceptable in their authors
view - nonlocal prediction of quantum physics [1, 6]. A lot has been
written on the EPR "paradox" and I won't add to this. I believe that
Einstein's reaction is easy to understand. Here is the man who turned
physics local, centuries after Newton wrote his alarming text, he is
proud of his achievement and certainly deserves to be. Now, only a few
years latter, non-locality reappears! Today one should add that quantum
nonlocality is quite a different concept from Newtonian nonlocality, but
Einstein did not fully realize this.
What Einstein and his colleagues saw is that quantum physics describes
spatially separated particles as one global system in which the two
particles are not logically separated. What they did not fully realize
is that this does not allow for signaling, hence it is not in direct
conflict with relativity. In the next section I'll try to present this
using modern terminology."

Small comfort since minimal changes in quantum theory, some quite
physical, do give signals outside the light cone. Furthermore curved
space-time allows consistent time travel to the past as shown by Igor
Novikov, Richard Gott and others.

"Most physicists didn't pay much attention to this aspect of quantum
physics. A kind of consensus established that this was to be left for
future examination, once the technologywould be more advanced. The
general feeling was that quantum nonlocality was nothing but a
laboratory curiosity, not serious physics."

Yes, this is what Sylvan Schweber told me at Brandeis in 1960-61 when I
independently saw that EPR seemed to require action at a distance
outside the light cone. Schweber and other faculty at Brandeis physics
department told me not to think about this problem.

"Young physicists may have a hardtime to believe that such an important
concept, like quantum nonlocality, was, during many decades, not
considered as serious. But this was indeed the real state of affairs: ask
any older professors, a vast majority of them still believes that it is
unimportant. Let me add two little stories that illustrate what the
situation was like. John Bell, the famous John Bell of the Bell
inequalities and of the Bell states, never had any quantum physics
student. When a young physicist would approach him and talk about
nonlocality, John's first question was: 'Do you have a permanent
position?' Indeed, without such a permanent position it was unwise to
dare talking about nonlocality! Notice that John Bell almost never
published any of his remarkable and nowadays famous papers [7] in
serious journals: the battle with referees were too ... time wasting
(not to use a more direct terminology). Further, if you went to CERN
where John Bell held a permanent position in the theory department and
asked at random about John's contributions to physics, his work on the
foundation of quantum physics would barely be mentioned (true enough, he
had so many other great contributions!)2.
Anyway, so quantum nonlocality remained for decades in the curiosity lab
and no one paid much attention. But in the 1990's two things changed.
First, a conceptual breakthrough happened thanks to Artur Ekert and to
his adviser David Deutsch [9]. They showed that quantum nonlocality
could be exploited to establish a cryptographic key between two distant
partners and that the confidentiality of the key could be tested by means
of Bell's inequality. What a revolution! This is the first time that
someone suggested that quantum nonlocality is not only real, but that it
could even be of some use. A second contribution came from the progress
in technology. Optical fibers had been developed and installed all over
the world. And Mandel's group at the University of Rochester (where I
held a one-year post-doc position and first met with optics) applied
parametric down-conversion to produce entangled photon pairs [10]. This
was enough (up to the detectors) to demonstrate quantum nonlocality
outside the curiosity laboratory. In 1997 my group at Geneva University
demonstrated the violation of Bell inequalities between two villages
around Geneva, see Fig. 1, separated by a little more than 10 km and
linked by a 15km long standard telecom fiber [11, 12] (since then, we
have achieved 50km [13]). So quantum nonlocality became politically
acceptable! But what is it? Let me introduce the concept using students
undergoing 'quantum exams".
2Another story happened to me while Iwas a young post-doc eager to
publish some work. In a paper [8]Iwrote 'A quantum particle may
disappear from a location Aand simultaneously reappear in B, without any
flow in-between". The referee accepted the paper under the condition that
this outrageous sentence is removed. This referee considered his
paternalist attitude so constructive that he declared himself to me:
'look how helpful I am to you' (admittedly, he was politically correct)."

See Robert Anton Wilson's "Cosmic Trigger" and Martin Gardner's "Magic
and Paraphysics" in the late 1979's where I introduce this idea as well.

"VI. QUANTUM EXAMS: ENTANGLEMENT
Assume that two students, Alice and Bob, have to pass some exams. As
always for exams, the situation is arranged in such a way that the
students can't communicate during the exam. Clearly however, they are
allowed, and even encouraged, to communicate beforehand. Alice and Bob
know in advance the list of possible questions, they also know that this
is a kind of exam allowing only a very limited number of possible
answers, often only a binary choice between yes and no. During the exam
Alice receives one question out of the list, let's denote it by x; Bob
receives question y. Finally, denote by a and b Alice and Bob's answers,
respectively. Hence, an exam is a realization of a random process
described by a conditional probability function, often merely called a
correlation P(a,b | x,y). Clearly, the choice of questions x and y are
under the professor's control. However, as all professors know, the
students' answers a and b are not! This is similar to experiments: the
choice as to which experiment to perform is under the physicist's
control, but not the answer given by Nature. In the following, we shall
consider three kinds of exams, in order to understand what kind of
constraints they set on the correlation P(a,b | x,y).
A. Quantum exam#1
In this first kind of quantum exam Alice is asked to tell which question
is given to Bob, and vice-versa. This is clearly an unfair exam! Why?
Because Alice and Bob are not supposed to communicate. How could they
then succeed with a probability greater than mere chance3? This simple
example shows that prohibiting signaling already limits the set of
possible correlations P(a,b | x,y) Notice that a correlation P(a,b |
x,y) is non-signaling if and only if its marginal probabilities are
independent of the other side's input... ...
|Sum over b of P(a,b | x,y) is independent of y
Sum over a of P(a,b | x,y) is independent of x|
B.Quantumexam#2
The second kind of quantum exam is closer to standard exams. Alice and
Bob are simply requested to provide the same answer whenever they
receive the same question. This is clearly feasible: we all expect that
good students give the same answer to the same question. It suffices that
they prepare for the exam well enough. Note that the quantum exam #2
under consideration here is even easier than standard exams, as there is
no notion of correct or incorrect answers. All that is required is that
Alice and Bob give consistent answers: it suffices that they jointly
decide in advance which answer to give for each of the possible
questions. Now, a central problem: Could Alice and Bob succeed with
certainty for such an exam #2 by other means, that is without jointly
deciding the answers in advance? Think about it. If you found an
alternative trick, then, if you are a student, you should use your trick
to pass the next examination: just apply your trick together with the
best student, you'll get the same mark as him/her4. And if you are a
professor and found a trick, then you should stop testing your student
with standard exams! Well, of course, there is no other trick, at least
none applicable to classical students.

3Somewhat surprisingly there is a strategy such that the probability
that both players succeed is 50%.
....

In summary, some exams require common strategies; in other words, some
observed correlations can't be explained except by common causes ...
Accordingly, quantum theory predicts that some tasks can be achieved
that can't be predicted by any local mechanical model, i.e. some exams
are passed with higher marks than classically possible. The fact that
such tasks were invented for the purpose of showing the superiority of
quantum physics doesn't affect the conclusion. Still, it is only once
some useful and natural tasks were found, concretizing the superior
power of quantum physics over all possible local strategies, that
quantum nonlocality became accepted by the physics community5.
5I wish someone establishes the statistics of the occurrences of the
words "Bell inequality" and "nonlocality" in Physical Re-

FIG. 1: Bernex and Bellevue are the two villages north and south of
Geneva between which our long-distance test of Bell inequality outside
the lab was performed in 1997, section V. The inset represent two player
that toss coins, as explained in section VII. In the real experiment the
coins were replaced by photons, the players by interferometers, their
right and left hands by phase modulators and head/tail by two detectors.
The experimental results are similar to that of the game, with weaker
but still nonlocal correlations.
VII. COIN TOSSING AT A DISTANCE
.... I bet that a phase transition happen in the early 1990's, after
Ekert's paper on quantum cryptography. In 1997 I started a PRL with the
sentence: 'Quantum theory is nonlocal.' and got considerable reactions
to what was felt as a provocative statement; today the same statement
can be found in many papers, not provoking any reaction."

Indeed Murray Gell-Mann says quantum theory is local in his book "The
Quark and the Jaguar." Murray opts for a many worlds interpretation that
he thinks is a loophole.

"... John Bell used to say "correlations cry out for explanations!"[16].

So, why are our two players that excited by the correlation they
observe? Note that locally, nothing interesting happens; in particular
there is no way for one player to infer from his data which hand the
other player chose. Even if one player decides to always use the same
hand, this has no effect on the statistics observed by his colleague.
Consequently, this game and the observed correlation do not imply any
signaling. So, why do we feel that this is impossible? Actually,
frankly, I do not know!"

In fact such signaling happens in normal consciousness. Microquantum
theory with this signal locality is violated in general quantum theory.
It is only found in special quantum theory. Signal nonlocality is the
analog of space-time curvature. Signal locality is the analog of global
flatness, i.e. special relativity. This is where I part company with
Lenny Susskind's theory in a fundamental way.

"Classical correlations are always explained by either of two kinds of
causes. The first kind is "signaling", one player somehow informs or
influences the other player. This is clearly not the case here, since we
assumed the players were widely separated in space (for the physicists
we may add "space-like separated"). The second kind of causes for
classical correlations is a common cause. For example all football
players simultaneously stop running, because the umpire whistled. This
kind of cause is precisely equivalent to the assumption of a common
strategy, as formalized by (2) and excluded for the present correlation
by Bell's inequality (4). Consequently, the correlation observed by our
two players is of a different nature. The big surprise is that anything
beyond the two classical causes for correlation exists! This is what
Einstein and many others had a hard time to believe. But, today, if one
accepts this as a matter of theoretical prediction and experimental
confirmation, then the next big question is 'why can't the correlation
observed by our hypothetical players not be observed in the real world?'
Indeed, quantum physics (and tensor products of Hilbert spaces) tell
us that Bell's inequality (4) can be violated, i.e. not all quantum
correlations can be explained by one of the two kinds of classical
causes for correlations, but quantum physics does not allow correlations
as strong as observed by our hypothetical players. Still, this game is
illustrative of quantum nonlocality, as we shall elaborate in section X

VIII. EXPERIMENTS: GOD DOES PLAY DICE, HE EVEN PLAYSWITH NONLOCAL DICE
Physics is an experimental science and experiments have again and again
supported the nonlocal predictions of quantum theory. All kind of
experiments have been performed, in laboratories [18] and outside [11,
12, 19], with photons and with massive particles [20], with independent
observers to close the locality loophole [11, 12, 17, 19, 21], with
quasi-perfect detectors [20] to close the detection loophole, with high
precision timing to bound the speed of hypothetical hidden communication
[22], with moving observers to test alternative models [23]
(multi-simultaneity [24] and Bohm's pilot wave [25])6. All these results
proclaim loudly: God plays dice. Note how ironic the situation is: the
conclusion "God plays dice" is imposed on us by the experimental
evidence supporting quantum nonlocality and by Einstein's postulate that
no information can travel faster than light. Indeed, as mentioned in
sub-section VIC, a violation of (4) with deterministic outputs leads to
signaling. Consequently, the experimental violation of (4) and the
no-signaling principle imply randomness [26, 27]."

I do not dispute what Gisin says for simple systems under the conditions
of all experiments done with simple systems. The living brain
experiments of Ben Libet, Dean Radin, and Dick Bierman suggest a break
down of the above "sub-quantum equilibrium" as described by Antony
Valentini.

"Actually, the situation is even more interesting: Not only does God
play dice, but he plays with nonlocal dice! The same randomness
manifests itself at several locations, approximating a+ b?xy better than
possible with any local classical physics model. A very small minority
of physicists still refuse to accept quantum nonlocality."

Trevor Marshall is one of them. Bernie Haisch's ZPE theory is based upon
Marshall's SED theory without quantum nonlocality. This is another
argument against Haisch's theory.

"They ask (sometimes with anger): 'How can the set of space-time
locations, out there, know about what happens in each other's without
any sort of communication?' I believe that this is an excellent
question! I have slept with it for years [28]. I summarize my conclusion
in the next section."
Bohm's answer is the nonlocal action of the quantum potential of the
pilot BIT wave on the IT particle.

IX. ENTANGLEMENT AS A CAUSE OF CORRELATION
Quantum physics predicts the existence of a totally new kind of
correlation that will never have any kind of mechanical explanation. And
experiments confirm this: Nature is able to produce the same randomness
at several locations, possibly space-like separated."

This explains how the total density of superfluid at absolute zero is
100% even though the condensate density is only a few %. Most of the
superfluid is virtual zero point energy with the same local randomness
all over the fluid. The superfluid is locally random whilst being
nonlocally coherent. Robert Becker introduced this idea of nonlocal
coherence with synchronized local randomness. I applied it to the
superfluid. He did not know of that application until we communicated by
e-mail late 2005.

"The standard explanation is 'entanglement', but this is just a word,
with a precise technical definition [29, 30]. Still words are useful to
name objects and concepts. However, it remains to understand the
concept. Entanglement is a new explanation for correlations. Quantum
correlations simply happen, as other things happen (fire burns, hitting a
wall hurts, etc). Entanglement appears at the same conceptual level as
local causes and effects. It is a primitive concept, not reducible to
local causes and effects.Entanglement describes correlations without
correlata [31] in a holistic view [32]. In other words, a quantum
correlation is not a correlation between 2 events, but a single event
that manifests itself at 2 locations.

Are you satisfied with my explanation of what entanglement is? Well, I am
not entirely! But what is clear is that entanglement exists. Moreover,
entanglement is incredibly robust! The last point might come as a
surprise, since it is still often claimed that entanglement is as
elusive as a dream: as soon as you try to talk about it, it evaporates!
Historically this was part of the suspicion that entanglement was not
really real, nothing more than some exotic particles that live for
merely a tiny fraction of a second. But today we see a growing number of
remarkable experiments mastering entanglement. Entanglement over long
distances [11, 12, 13, 19, 33], entanglement between many photons [34]
and many ions [35], entanglement of an ion and a photon [36, 37],
entanglement of mesoscopic systems (more precisely entanglement between
a few collective modes carried by many particles)[38, 39, 40],
entanglement swapping [41, 42, 43], the transfer of entanglement between
different carriers [44], etc. In summary: entanglement exists and is
going to affect future technology. It is a radically new concept,
requiring new words and a new conceptual category.

6The conclusion that follows from all these experiments is so important
for the physicist's world-view, that an experiment closing
simultaneously both the locality and the detection loophole is greatly
needed.

X. FROM QUANTUM NONLOCALITY TO MERE NONLOCALITY
So far we have seen that quantum physics produces nonlocal correlations.
And so what? Ok, this can be used for Quantum Key Distribution and other
Quantum Information processes, but that doesn't help much to under-stand
non-locality. Conceptually, one would like to study non-locality without
all the quantum physics infrastructure: Hilbert spaces, observables and
tensor products. Not too surprisingly, once the existence of
non-locality was accepted, the conceptual tools to study it came very
naturally. Actually, the tools were already there, in the mathematics
[45] and even the physics [26, 27] literature, waiting for a community
to wake up! The basic tool is simple, doesn't require any knowledge of
quantum physics and allows one, so to say, to study quantum nonlocality
"from the outside", i.e. from outside the quantum physics infrastructure.
Let us go back to the quantum exam #3 (subsection VIC). Assume that
Alice and Bob are not restricted by quantum physics, but only restricted
by no-signaling. Consequently, they would fail the quantum exam #1. But
under this mild no-signaling condition they could perfectly succeed in
the quantum exam #3: Alice and Bob would each output a bit which locally
looks perfectly random and independent from their inputs -hence there
would be no signaling - yet their 2 bits would satisfy a+ b= xy, exactly
as in the coin tossing game of or as a NL-machine (a Non-Local
machine7). The idea of these terminologies is to emphasize the
similarities between quantum measurements on 2 maximally entangled
qubits and the correlation (5): in both cases the outcome is available
as soon as the corresponding input is given (Alice knows a as soon as
she inputs x into her part of the machine and similarly Bob knows b as
soon as he inputs y, there is no need to wait for the other's input) and
in both the quantum and the PR-box cases the "machine" can't be used
more than once (once Alice has input x, she can't change her mind and
give another input). Notice a third nice analogy, neither the quantum
nor the NL machines allow for signaling. Indeed, in all cases the
marginals are pure noise, independently of any input.
.... First we shall consider the so-called quantum no-cloning theorem and
see that it is actually not a quantum theorem, but a no-signaling
theorem. The next natural step is to analyze quantum cryptography, whose
security is often said to be based on the no-cloning theorem, and as we
would expect by now, we shall find 'non-signaling cryptography'. Finally,
we consider the question of the communication cost to simulate maximal
quantum correlation. But before all this we need to recall some facts
about non-signaling correlations."

Go to original paper.
B. No-cloning theorem
Details can be found in [47], as here we would merely like to present
the intuition. Let us assume that Alice (input and output bits x and a,
respectively) shares the correlation (5) both with Bob (bits y and b)
and with Charly (bits z and c): a+ b = xy and a+ c = xz. Note that this
situation is different from the case where Alice would share one
'machine' with Bob and share another independent 'machine' with Charly:
in the situation under investigation Alice holds a single input bit x
and a single output bit a. We shall see that the assumption that Alice's
input and output bits x and a are correlated both to Bob and to Charly
leads to signaling. Hence in a Universe without signaling, Alice can't
share the correlation (5) with more than one partner: the correlation
can't be cloned.
In order to understand this, assume that Bob and Charly come together,
input y= 1 and z= 0, and add their output bits b+ c. According to the
assumed correlations and using the modulo 2 arithmetic a+a=0, one gets:
b + c= a + b+ a + c = xy+ xz= x. Hence, they could determine from their
data that Alice's input bit is x, i.e. Alice could signal to them!
A natural question is how noisy should the correlation (5) be to allow
cloning? The answer is interesting: as long as the Alice-Bob correlation
violates the Bell inequality (4), the Alice-Charly correlation can't
violate it; if not there is signaling.
We have just seen that the CHSH-Bell inequality (4) is monogamous, like
well kept secrets. Let's now see that this is not a coincidence!
C. Non-signaling cryptography
In 1991 Artur Ekert's discovery of quantum cryptography [9]based on the
violation of Bell's inequality changed the (physicist's) world:
entanglement and quantum non-locality became respectable. Now, as we
shall see in this subsection, the essence of the security of quantum
cryptography does not come from the Hilbert space structure of quantum
physics (i.e. not from entanglement), but is due to no-signaling
nonlocal correlation! The fact that quantum physics offers a way to
realize such correlation makes the idea practical. However, if one would
find any other way to establish such no-signaling nonlocal correlations
(a way totally unknown today), then this would equally well serve as a
mean to establish cryptographic keys [51]."

The more interesting question is what happens when there is signaling as
in Antony Valentini's general quantum theory without "sub-quantal
equilibrium."? No more cryptography?

"Let us emphasize that the goal is to assume no restriction on the
adversary's power, i.e. on Eve, except no signaling9[52]. Obviously, if
one assumes additional restrictions on Eve, like restricting her to
quantum physics, then Alice and Bob can distill more secret bits from
their data. But qualitatively, the situation would remain unchanged.

8More precisely, 8 is the dimension of the space of non-signaling
correlations [50].

|
9No-signaling should be understood here as in the previous subsection on
the no-cloning theorem. That is, even if two parties joint, for example
Eve and Bob come together, then they should not be able to infer any
information about the third party's input,
e.g. Eve and Bob should not have access no Alice's input.
... Can Alice and Bob exploit such a correlation for cryptographic usage
secure against an arbitrary adversary who is not restricted by quantum
physics, but only restricted by the no-signaling physics? The full
answer to this fascinating question is still unknown.
...
Let's come back to the real central question: How does Nature manage to
produce random data at space-like separated locations that can't be
explained by common causes? The idea that Nature might be exploiting
some hidden communication (hidden to us, humans) is interesting. With my
group at Geneva University we spent quite some time trying to explore
this idea, both experimentally and theoretically. We could set
experimental bounds of the speed of this hypothetical hidden
communication [22]. We also investigated the idea that each observer
sends out hidden information about his result at arbitrary large speeds
as defined in its own inertial reference frame [23]. The measured bounds
on the speed of the hypothetical hidden communication were very high and
the latter assumption contradicted by experiments. Also our theoretical
investigation cast serious doubts on the existence of hidden
communication. Analyzing scenarios involving 3 parties we could prove
that if all quantum correlations would be due to hidden communication,
then one should be able to signal (i.e. the hidden communication do not
remain hidden) [63, 64]! Hence, the only remaining alternative is that
Nature exploits both hidden communication and hidden variables: each one
separately contradicts quantum theory, but both together could explain
quantum physics. However, this seems quite an artificial construction.
Hence, let's face the situation: Nature is able to produce nonlocal data
without any sort of communication. But is she doing so using all the
quantum physics artillery? Aren't there logical building blocks of
nonlocality? A partial answer follows.
....
i.e. from the perspective of future physical theories (assuming these
will keep Einstein's no-signaling constraint) and no longer from the
perspective of the old classical mechanical physics. But there is still
a lot to be done! For instance, it is surprising (and annoying in my
opinion) that one is still unable to simulate measurement on partially
entangled states using the nonlocal correlation (actually we could prove
that this is impossible witha single instance ofthe correlation, but
there is hope thatone can simulate partially entangled qubit pairs with
2 instances [67]). Let me emphasize that all of today's known simulation
models for partially entangled qubits include some sort of
communication13[62], let's say from Alice to Bob. Consequently, in all
these models Bob can't output his results before Alice was given her
input. This contrasts with the situation in quantum measurements where
Bob doesn't need to wait for Alice (he does not even need to know about
the existence of Alice) and with the simu ation model for maximally
entangled qubits using the PR-box. It would be astonishing if partially
entangled state could not be simulated in a time-symmetric way [69].

13Using the reduction of an OT-box (Oblivious Transfer to a PR-box) [68]
one can simulate any 2-qubit state with one OT-box.

XI. CONCLUSION
The history of non-locality in physics is fascinating. It goes back to
Newton (section II. It first accelerated around 1935 with Einstein's EPR
and Schrodinger cat's papers. Next, it slowly evolved, with the works of
John Bell, John Clauser and Alain Aspect among many others, from a mere
philosophical debate to an experimental physics question, or even to
experimental metaphysicsas Abner Shimony nicely put it [70]. Now, during
the last decade, it has run at full speed. Conceptually the two major
breakthroughs were, first Artur Ekert's 1991 PRL which strongly suggests
a deep link between non-locality and cryptography, section XC. The
second breakthrough, in my opinion, is the PR-box, section XA, the
understanding that non-signaling correlations can be analyzed for
themselves, without the need of the usual Hilbert space artillery, thus
providing a simple conceptual tool for the unraveling of quantum
non-locality. We have reviewed that the no-cloning theorem, the
uncertainty relation, the monogamy of extreme correlation and the
security of key distribution, all properties usually associated to
quantum physics are actually properties of any theory without signaling,
section X. In particular we emphasized that the second breakthrough, the
PR-box, allows one to confirm the first breakthrough: there is an intimate
connection between violation of a Bell inequality and security of
quantum cryptography.
And relativity, can it be considered complete? Well, if nonlocality is
really real, as widely supported by the accounts summaries in this
article, then all complete theories should have a place for it. Hence,
the question is: 'Does relativity hold a place for non-signaling
nonlocal correlations?'.
Acknowledgment
This article has been inspired bytalks I gave in 2005 at the IOP
conference on Einstein in Warwick, the QUPON conference in Vienna, the
Annus Mirabilis Symposium in Zurich, le seminaire de l'Observatoire de
Paris and the Ehrenfest Colloquium in Leiden. This work has been
supported by the EC under projects RESQ and QAP (contract n.
IST-2001-37559 and IST-015848) and by the Swiss NCCR Quantum Photonics.
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