SEVEN USES FOR QUANTUM ENTANGLEMENT


ABSTRACT: An important feature of two-particle systems is quantum entanglement (QE). Actions carried out on one QE particle seem to affect its distant partner instantly as through they were never separated. Schrödinger called quantum inseparability not one but the process in which quantum theory differs most from classical expectations.

QE is necessary for premeasurement, for establishing the von Neumann chain between system and observer, useful for achieving decoherence by interaction with the environment. Attribute coupling and context coupling seem to imply a new type of connection. stronger than classical correlation. The necessarily non-local nature of this connection is established by Bell's theorem, limited to Reality and Theory by Eberhard's Proof.

Quantum entanglement combined with simple ESP or PK powers leads immediately to a primitive type of time machine.


SEVEN USES FOR QUANTUM ENTANGLEMENT



According to conventional wisdom, the single-particle wavefunction |A> encodes all knowable info concerning the (statistical) results of any possible measurement carried out on an ensemble of similarly prepared examples of A: A1, A2, A3, etc. For this one-particle state, the crucial Quantum Reality Questions take the form: 1) What is the physical state of a single system A whose mathematical representation is |A>? (How can we best conceptualize the nature of one unobserved quantum system?) 2) What is a measurement? (How does one physical state A produce human-observable indications of its attributes?). These unsolved questions--the core of physicists' quantum reality crisis--become even more acute when we move up in complexity to quantum two-body systems.

Consider system A which can possess two possible attributes a1 and a2 and system B which possesses two attributes b1 and b2. If these systems are independent their combined wavefunction |C> is written in product form |C> = |A>|B>. Now let us imagine that both A and B exist in some equiprobable superposition of their attributes. In this case the product state becomes:

|C>ind = (|a1> + |a2>) (|b1> + |b2>)

= |a1> |b1> + |a1> |b2> + |a2> |b1> + |a2> |b2> 1)

Suppose some (unspecified) process now causes the cross terms to vanish. The resulting wavefunction |C>ent is the simplest example of an entangled state . There is no reference frame in which this entangled system can be factored into a product of two states.

|C>ent = |a1> |b1> + |a2> |b2> 2)

The physics of this deceptively simple two-state has much to teach us about the nature of quantum theory and the world. The remainder of this essay is a brief review of seven indispensable features of quantum entanglement.

PRE-MEASUREMENT
In order to perform a measurement on an invisible system A, we must find some visible system B such that when A has the attribute a1 then B will display the attribute b1; Also when A is a2 then B is b2. Systems such as B are necessary for making a measurement on A but not sufficient. To complete the measurement the attribute(s) of system B (which I will call a "probe") must somehow end up as the contents of some human consciousness.

Suppose the probe B to be in neutral state |b0> and the system A to be in a superposition state |A> = |a1> + |a2>. After interaction the probe-system wavefunction finds itself in the entangled state |C>:

|C> = |a1> |b1> + |a2> |b2> 3)

We see that "probing" a superposed quantum state places the probe itself in a superposition. If the probe is macroscopic such a superposition is called a "Schrödinger Cat" after the Austrian physicist Erwin Schrödinger who imagined in 1935 splitting a cat by entangling it with a quantum system. In terms of this entangled Cat the two Quantum Reality Questions take the form: 1) What is the real status of the S-Cat (probe B) when its description is a superposition? 2) How and why do we observe only one term (either b1 or b2) but never both? (Why are S-Cats inevitably invisible?)

MEASUREMENT
In order for the attributes of probe B to appear in human consciousness the probe must be connected to the brain of the observer by a chain of two-state systems D, E, F, G where D may be photons, E the state of the observer's retina, F the state of the observer's optic nerve and G the state of some portion of the visual cortex. In order for an observation of system A to occur these intermediate systems must have the convenient "probe property" that during interaction their two states, |d1 and |d2> for instance, become correlated with the appropriate B probe states |b1> and |b2>. For a true measurement to occur an unbroken chain of entanglement must extend from the invisible quantum system A to some part G of the observer's brain:

|M>ent = |a1>|b1>|d1>|e1>|f1>|g1> + |a2>|b2>|d2>|e2>|f2>|g2> 4)

This multistate entanglement is called the "von Neumann chain" after John von Neumann's famous analysis of the "measurement problem".

Von Neumann asked: where in this chain does the wavefunction "collapse" from the superposition represented by Eq 4) into one or the other term of the entanglement to agree with the fact that we always perceive that system A is either in state |a1> or |a2> but never both? Von Neumann reluctantly concluded that, since all the links of the chain are physical objects, they must obey Schrödinger's equation which treats both terms of the superposition even-handedly (no collapse). Thus either some physical objects are not subject to the S-equation (a speculation that is entirely groundless at present) or some process outside of physics accomplishes the collapse. The most logical candidate for a collapse-inducing non-physical process is human consciousness. Thus, in the von Neumann picture, two parallel von Neumann chains are reduced to one by the action of consciousness--mind is a necessary part of physical reality, a conclusion developed further by Fritz London, Edmund Bauer, Eugene Wigner, Henry Stapp, Amit Goswami and Casey Blood.

DECOHERENCE
For concreteness imagine system A to be a single photon split by a beamsplitter into two paths a1 and a2. The two paths are then brought together on a phosphor screen and the states |a1> and |a2> represent the possibility of the photon appearing in region 1 or region 2 on the screen. Assume that regions 1 and 2 overlap so that there is opportunity for interference. Assume further that conditions are such (path length, coherence length, screen resolution, etc) that interference fringes are actually observed.

|A> = |a1> + |a2> 5)

To test for interference we form the density matrix |A><A| from the wavefunction (Eq 5) and look for cross terms:

|A><A| = |a1><a1| + |a2><a2| + |a1><a2| + |a2><a1| 6)

The last two terms represent interference twixt paths a1 and a2.

Now suppose that on its way to the screen photon a2 interacts with a system B in an maximally non-disturbing way such that: 1) the initial state |b1> and the final state |b2> of B have the same energy, so no energy is extracted from photon A; 2) the phase of photon A is likewise undisturbed by this interaction: as B goes from state |b1> to state |b2>, the photon goes from state |a2> to |a2>, that is, it is left entirely unmolested. Whether such a gentle interaction is physically realizable may be questionable, but in the spirit of a Thought Experiment let's imagine photon A to be probed by B in such a maximally undisturbing manner and simply calculate the consequences.

When photon traverses path a1, B remains in state |b1>; when photon traverses a2, system B is placed in state |b2> while system A is (magically?) left undisturbed. This (non-disturbing for A) interaction places states A and B in a mutually entangled state |C>ent.

|C>ent = |a1>|b1> + |a2>|b2> 7)

To calculate the possibility of interference we form the density matrix and look for cross terms.

|C><C| = |a1>|b1><a1|<b1| + |a2>|b2><a2|<b2|

+ |a1>|b1><a2|<b2| + |a2>|b2><a1|<b1| 8)

To isolate the photon variables a from the "probe" variables b, we take the partial trace of the density matrix over the b variables:

|C><C|photon = <b1|C><C|b1> + <b2|C><C|b2> 9)

If the probe states |b1> and |b2> are orthogonal (<b1|b2> = 0), this reduces to:

|C><C|photon = |a1><a1| + |a2><a2| 10)

This is the density matrix for an incoherent superposition of states |a1> and |a2>. We see that interference vanishes whenever a system becomes entangled with a pair of orthogonal states. Thus this special sort of interaction (entanglement) is sufficient to destroy interference despite the facts that: 1) systems |b1>, |b2> need not be macroscopic--just orthogonal; 2) system B need not be observed; 3) system A is "undisturbed" by the entanglement.

One strategy for attacking the measurement problem (Zurek, Hartle, Gell-Mann) is to search for types of interactions that will "decohere the wavefunction" so that interference terms vanish leaving the system in a state described--as in Eq 10--by an incoherent mixture of diagonal density matrix elements with no cross terms. Since no interference terms are present, the probabilities generated by this sort of density matrix are formally equivalent to classical (dice-style) probabilities. It is then easy for some thinkers to convince themselves that the reality which these matrix elements represent has become a classical-style reality--that, in other words, decoherence itself is sufficient to "collapse the wavefunction".

This argument is dubious at best: even if incoherent, the elements of the density matrix continue to represent possibilities not actualities: an explicit collapse mechanism still seems necessary. (I have expressed this objection elsewhere by saying that no amount of mixing can convert black sand and white sand into grey sand). And even if decoherence can be somehow be construed as collapse, what states does the system collapse into? Is unpolarized light (a typical incoherent mixture of two states) "in reality" a classical mixture of H and V photons? Or is it a classical mixture of R and L photons?

In typical decoherence/collapse schemes Entanglement-with-the- Environment is invoked to achieve the necessary decoherence. However this analysis shows that systems far less complicated than the entire environment suffice to eliminate the system's phase: for example, solid entanglement with even a single atom will completely erase the photon's phase. In light of this result it is a marvel that interference experiments are possible at all! Consider the photon in path a1 interacting with a mirror containing trillions upon trillions of light-responsive atoms. As it bounces off this mirror its phase will be completely destroyed if it entangles (even in a non-destructive manner) with just one of the many myriads of mirror atoms. Mirrors are truly marvelous (as are lenses) in that they are macroscopic objects that can strongly interact with and change a photon's state of motion without the slightest hint of entanglement.

This analysis of photon phase loss shows that it is entanglement not "disturbance", nor "observation" that destroys the interference pattern during measurement. "Disturbance" is a red herring: even interactions purposely designed (as above) to be maximally non-disturbing can destroy interference. Likewise with observation. Altho some mind could in principle observe system B and infer the state of entangled system A, no such observation is necessary for A's interference terms to vanish.

An independent particle's wave function possesses intrinsic amplitude and phase representing the probability of results of measurements made on that particle alone. On the other hand, an entangled particle does not possess its own wavefunction. The two-particle system is in a definite quantum state but the particles themselves are not. Each partner in the entanglement is described by conditional not intrinsic probabilities. Participation in quantum entanglement entails a kind of "loss of self" for each participant, a phenomenon not unheard of in certain intimate human connections.

COUPLED CONTEXTS
In an entangled state the attributes of system A are coupled one-to-one with the attributes of system B. Thus the observation that system B is in state b1 gives certain knowledge that system A is in state a1. If systems A and B are spatially separated, entanglement allows us to discover the properties of a far-away system by observations made locally. This ability is not initially surprising because it is similar to situations of classical correlation. If I seal a silver coin in one envelope and a gold coin in another and send one envelope to Seattle, the other to Sydney, the moment she opens her Seattle packet, she knows the state of the coin in Sydney. But quantum systems are more subtle than coins because of the "meter option"--each observer's ability to choose at the last moment what attribute to measure. The wavefunction tells us not what a system is, but how it will appear to be in any conceivable experimental context. Until you have provided a particular context, the wavefunction is silent not only about the values of particular attributes, but even about what kinds of attributes the system may be said to possess.

For instance consider a system consisting of two polarization-correlated photons P and p which are moving apart from one another at the speed of light and are observed with polarization meters located (say) on Earth and Pluto. These meters can be adjusted to measure an infinite number of polarization dichotomies, for instance H-or-V (Horizontal or Vertical) or D-or-S (Diagonal or Slant) or R-or-L (Right or Left circular Polarization). When both meters are set to provide an H/V context the entangled photon wavefunction |C> can be written:

|C> = |H>|h> + |V>|v> 11)

An observation of H-polarized photon P on Earth tells us instantly that Pluto photon p will be measured to have polarization h. However we could have chosen to measure D/S polarization at both stations where |D> = |H> + |V> and |S> = |H> - |V>. In terms of this measurement context the same coupled photon state can be written:

|C> = |D>|d> + |S>|s> 12)

Recalling the decohering feature of entanglement, we can write the density matrices on Pluto for these two cases: 1) measuring H/V on Earth; 2) measuring D/S on Earth:

Case 1: |C><C|Pluto = |h><h| + |v><v|
13)
Case 2: |C><C|Pluto = |d><d| + |s><s|

These results seem to imply that if I make a H/V measurement on Earth the photons on Pluto turn into an incoherent mixture of h and v photons. If I make a D/S measurement on Earth, the Pluto photons obediently become an incoherent d/s mixture.

Now mathematically these two expressions are exactly equivalent, but what about "reality"? Does changing the context on Earth actually cause a physical change in the distant photons on Pluto?

BELL'S THEOREM
In 1963 Irish physicist John Stewart Bell investigated the question of the effect of distant measurement contexts on local realities. Bell assumed that change of context on Earth does not change photon properties on Pluto and derived a simple condition that the Earth/Pluto polarization results must satisfy if this so-called "locality assumption" is correct. Quantum-mechanical calculations and experiments done at Berkeley (Clauser), Paris (Aspect) and elsewhere show that the Bell condition is strongly violated. Thus Bell's locality assumption is false. In light of Bell's result one can reasonably conclude that a change in context on Earth instantly changes photon facts on Pluto. Berkeley physicist Henry Stapp has called Bell's theorem "the most profound result in science".

Using Immanuel Kant's convenient three-fold division of knowledge into Appearance, Reality and Theory where Appearance is the sum of what we perceive--both inner and outer; Reality the more-or-less hidden causes behind Appearance, and Theory the stories we make up about both Appearance and Reality, we can place Bell's theorem in its proper context. Bell's theorem is not about Appearance nor Theory; it is about Reality. Bell's theorem states that no model of Reality in which photons on Pluto are unaffected by change of context on Earth can explain the quantum facts.

Bell proves that Reality is "non-local". What about Theory and Appearance?

Simple inspection shows quantum theory to be non-local. The unitary transformation (representing a change in Earth context) produces an immediate change in the distant waveform representing the Pluto photons. So Theory is non-local. What about Appearance? (It should be noted here that Bell's theorem is based only on logic and experimental facts: thus if quantum theory should someday be superceded by another kind of mathematical story, Bell's theorem would still be valid.)

Looking at the Pluto photons we see a random mixture of two types of polarization (whichever polarization pair we chose to measure) no matter what polarization context is chosen on Earth. Thus Appearance (in this situation at least) is stubbornly local.

EBERHARD'S PROOF
Generalizing from this simple two-photon case, Berkeley physicist Philippe Eberhard proved that (if quantum mechanics is correct) all Quantum Appearances must be local. Here the term "Quantum Appearances" means "statistical averages".

A quantum measurement consists always of individual events (which we might call "primary datums" (PDs) out of which one can form many kinds of statistical averages (SAs). One of the unquestioned dogmas of quantum theory is that the PDs are utterly random, lawless, totally outside the laws of physics or any other laws. Only the statistical averages (SAs) are subject to laws, and these laws are what we call quantum theory.

Eberhard's Proof shows that no change on Earth can change a statistical average on Pluto. So quantum theory is statistically local.
It seems intuitively obvious that any statistically local theory could easily be given a local PD underpinning. One of the surprises of Bell's theorem is that for entangled quantum states no such local PD underpinning is even conceivable.

One way of understanding the subtle relationship between locality, non-locality, SDs and PDs is to imagine that the PDs--the raw quantum jumps--actually are non-local: a change in Earth context actually does (in "reality") change individual quantum events on Pluto. However these Plutonian events are random so this Earth-induced "change" involves replacing one inscrutable random sequence by another sequence equally random. No statistical test can distinguish between these two sequences: "Although there are many kinds of order, there is only one kind of randomness". Thus (in this way of thinking) it is easy to send faster-than-light messages from Earth to Pluto using quantum entanglement. However these messages cannot ever be decoded because they are encrypted into utterly random-appearing sequences to which only nature holds the key..

MIND OVER MATTER
Eberhard's Proof shows that altho Earth and Pluto may be instantly connected in Reality, it is impossible in the world of Appearance using current physical processes to send faster than light messages via the quantum entanglement channel. However suppose we introduce processes that lie outside of conventional physical measurements. In particular could one apply ESP or PK locally to a quantum-entangled system and use this combination of local mind power and distant quantum links to send signals FTL in the realm of Appearance?

Physicist Helmut Schmidt in San Antonio has shown that certain individuals seem to be able to alter quantum-random sequences with their intentions. If this is a real (PK) effect, one could use it to send FTL messages to Pluto by simply setting both contexts to H/V. When Helmut on Earth signals a dash by mentally increasing H events on Earth, the increased h events on Pluto would represent a decodable message. Thus local PK plus entanglement would suffice to send FTL messages.

The time-machine aspects of such an FTL transmission scheme would not go unnoticed and perhaps the fact that the "Schmidt effect" will lead to temporal paradoxes is a sufficient argument to deny its existence. But also perhaps not. The Schmidt effect plus quantum links may represent the simplest time machine that could be constructed with 20th-century technology.

Consider the following quantum facts: when an H photon encounters an H/V detector it will certainly register H; when the same photon encounters a D/S detector it will randomly register as D 50% of the time and 50% of the time as S. Now suppose the existence of the following kind of (local) ESP ability. For a incoming photon entering a H/V detector the psychic guesses H, V or "don't know". We further suppose that when the photon is either D or S (that is, undecided in terms of H/D polarization) that the psychic has no edge over nature: he/she can only predict the results of events which are certain to happen. Then, for those events where the psychic scores greater than chance, the folks on Pluto know that the Earth context is H/V; otherwise the Earth context is S/D. Thus a certain kind of local ESP on Pluto in combination with a quantum link to Earth would produce a human-usable FTL connection over grand distances. Again the possibility of using this link as a time machine would not go unnoticed.

So local quantum-event PK on Earth can send FTL messages to Pluto as a pattern of deviation of H/h events from 50% . Likewise a certain variety of local ESP on Pluto can decode FTL messages from Earth encoded as a pattern of H/V and D/S contexts.

CONCLUSION
Most of the information collected here is well-known. What is new is its assembly in one place under the rubric of quantum entanglement. I have shown how essential QE is for the Premeasurement process (the formation of Schrödinger cats), in the Measurement process itself (establishing a von Neumann chain between system and observer), in the process of Decoherence which makes quantum possibilities look (at least formally) like classical probabilities (Entanglement Decoherence), in the suggestive property of Coupled Contexts in which distant influences seem to propagate instantly across spacetime (at least in Theory).

Bell's theorem uses entanglement to show that Reality as well as Theory is non-local while Eberhard proves that, if quantum mechanics is correct and complete, Appearances must remain stubbornly local. Finally I show that quantum Appearances are balanced so precisely on the edge of non-locality that the application of simple kinds of local ESP or PK suffices to make the Appearances themselves as non-local as the Reality which supports them. In this mind-over-matter context quantum entanglement might be exploited to construct a crude sort of stone-age time machine.




--NICK HERBERT
AMY PROJECT