# Is quantum entanglement functionally equivalent to a measurement?

I saw the following talk the other day: http://www.youtube.com/watch?v=dEaecUuEqfc&feature=share

In it, Dr. Ron Garret posits that entanglement isn't really that "special" of a property. He argues (and shows) that the mathematics behind it is analogous to the math behind measurement.

Is this true? There seems to be a lot of hoopla around quantum entanglement (including people that argue it could facilitate faster-than-light (FTL) communication). Is this excitement about the entanglement properties of some elementary particles unwarranted? Just looking for some clarification.

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"including people that argue it could facilitate faster-than-light (FTL) communication" I've never heard an educated physicist make that claim. Reference? – DanielSank Jun 24 '15 at 5:05
One more thing: in quantum mechanics measurement and entanglement are intimately related. That said, measurement in quantum mechanics is not simple at all, so pointing to that intimacy as evidence that entanglement is not special is a false logical step. Quantum entanglement is very different from anything that happens in classical physics, so I would say that the "hoopla" is at least partially warranted. – DanielSank Jun 24 '15 at 5:07
This topic is discussed a bit in somewhat lay terms in chapter 1 of my thesis. – DanielSank Jun 24 '15 at 5:37

Quantum entanglement and measurement are different point of views of the same underlying physical phenomena, say, the most distinct feature of the evolution of coupling between two physical systems.

From an external point of view, when two physical systems interact, they become entangled. This apply even if one of the systems is large and semi-classical (say, a photon detector). Regardless of the scale of the systems, when there is an interaction, the total system keeps evolving under an unitary propagator, which respects time symmetry.

From the point of view of each system, the coupling does not seem unitary at all; it seems like the other system suddenly collapsed to a random eigenstate of the coupling perturbation. Part of the quantum information that existed in the other eigenstates disapeared and became physically inaccessible. This is how we perceive measurement.

Regrettably, quantum entanglement cannot, by itself, allow FTL communication. The reason is that it produces correlation between measurements far away, but you still are unable to pick which definite state of the entangled superposition will the particles be.

To summarize, if you are one of two entangled systems, what you will see as an observer (after performing repeated experiments where the 'quantum' system is prepared in the same initial configuration system, something that obviously cannot be done to you, the observer) is that the particle states that the observer sees, seem to be probabilistic in nature, instead of behaving like a deterministic wave amplitude. That randomness is entirely associated to the subjective perspective of the entanglement process, and we call such processes, measurements

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Regarding your last paragraph: that is not the method by which the author posits FTL communication. Not by picking the state the superposition will collapse to, but by turning on or off the superposition itself. I asked a related question (physics.stackexchange.com/questions/55028/…) to which I never got a satisfactory answer, if you care to take a crack at it. – user1247 Mar 30 '13 at 19:28
hi user1247, Lubos answers are never satisfactory, but they are correct in the huge majority of cases :-) the problem is exactly what he said in his last paragraph: entanglement superposition is never seen locally; local measurements look as random as random gets. If you don't compare those local measurements with the measurements in the entangled pair, you'll never be able to notice that there was entanglement. Hence there is nothing that you can do remotely that will change the statistical distribution of remote events: all those events look correlated when compared with the remote measureme – lurscher Mar 31 '13 at 4:16
Thanks. Do you know why entanglement superposition is never seen locally? I'm very confused about this point, because how then, for example, can we ever see interference effects? Isn't each photon we see interfering in the usual double slit experiment ultimately entangled with some other photon or electron in the past? – user1247 Mar 31 '13 at 9:19
@user1247 That statement that entanglement isn't seen locally could be put like this: unless you have both pieces of a two-piece entangled system you absolutely cannot ever measure any of the "quantum" effects of that entanglement. If you only have one of two entangled particles, what you will see (upon repeated experiments with identically prepared pairs of entangled particles) is that your particle seems to be classical instead of quantum. This is a somewhat complex idea which I can't explain in a comment box :( – DanielSank Jun 24 '15 at 5:27
If you are one of two entangled systems, what you will see (upon repeated experiments where the 'quantum' system is prepared in the same system, but obviously the observer can't be prepared in the same state over and over) is that your particle states seem to be probabilistic instead of behaving like a deterministic wave amplitude – lurscher Jun 24 '15 at 16:54

It is difficult to say what it would mean for entanglement to be "the same as measurement", given that entanglement is essentially the phenomenon of the measurement outcomes of two systems being apparently random, but correlated to each other, in more than one basis of measurement. (Entanglement does exist as a concept independently of the measurement process — a pure state of two systems is entangled if and only if it does not factor as a tensor product, for example — but the "physical" significance of this is that the observables on the two factors will have correlated expectation values.) To quote a reasonably well-worded paragraph from the introduction to the Wikipedia article on entanglement:

Quantum entanglement is a form of quantum superposition. When a measurement is made and it causes one member of such a pair to take on a definite value (e.g., clockwise spin), the other member of this entangled pair will at any subsequent time be found to have taken the appropriately correlated value (e.g., counterclockwise spin). Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may have been separated by arbitrarily large distances.

Regardless of the reason for this correlation of measurement outcomes, what characterizes entanglement as distinct from "classical randomness" is precisely that the measurement outcomes are correlated in a way which is not straightforwardly explainable in terms of local hidden variables, unless your theory of particle behaviour allows faster-than-light signalling between particles. The "hoopla" comes from attempts to reconcile this in a way that we can picture in terms of classical probabilities, or from explicit rejections of the possibility that we can find such a reconciliation.

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A measurement is an interaction that allows some information about a quantum system to be copied. (The information that can be copied is something like the value of one particular observable or POVM, not the whole state.)

An entangled state is just a state that can't be written as a product of the state of each system. So $|a\rangle_1|a\rangle_2$ is not entangled but $|a\rangle_1|a\rangle_2+|b\rangle_1|b\rangle_2$ is entangled where $a\neq b$.

If you measure a system then the resulting state is typically an entangled state between the measured system, the measuring instrument and the environment (you, the air, photons that reflect from a computer screen displaying the measurement result and other similar stuff): $$|a\rangle_S|a\rangle_M|a\rangle_E+|b\rangle_S|b\rangle_M|b\rangle_E+\dots$$ However, the entanglement can't be used to do any particularly interesting experiments like looking for Bell correlations because to do such experiments you would have to be able to control the environment.

Entanglement is entirely a result of local interactions and Bell correlations can be explained entirely by local interactions, see

http://arxiv.org/abs/quant-ph/9906007

There is no prospect of using entanglement for non-local communication, because it does not involve any non-local processes.

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+1 for showing the math! – matao Nov 4 '15 at 8:25

Let us start from the beginning.

Elementary particles are quantum mechanical entities. They can be described with the quantum mechanical solutions of the appropriate equations for the set up under consideration with the constants taken from the boundary conditions of the problem. In this it is not different than the situation with classical mechanics problems. The difference is that it is not a deterministic solution, the square of the mathematical solution gives the probability of finding the system in a specific state if a measurement is done.

Thus a measurement means picking an instance from the probability distribution for the specific problem.

Take the double slit experiment. An electron is arriving at two slits. The quantum mechanical problem is set up by the position of the slits, the size of the slits and the fields defined at the edges of the slit. It will not be easy to write the exact equations, but the experiment picks by a measurement, the (x,y) of the electron at the screen at distance z.

At the top, the individual hits/measurements look random. At the bottom an interference pattern is observed. The interference pattern is the measurement of the wave function squared , and it displays the entanglement of the electron with the geometry and fields of the two slits.

Measurement is a single instance that contributes to the probability pattern. Entanglement is what is displayed after the fact , when many measurements are performed and the entanglement can be displayed.

Both depend on the functional form of the mathematical solutions of the specific equations. The measurement of the probability distribution displays the entanglement in this example. If one has a clean and clear mathematical solution then the probability distribution is known, and thus the entanglement of the system, i.e. the functional dependence of the wavefunction on the variables and the quantum numbers can be predicted.

Coordinates, as in the example above, are continuous and the entanglement contained in the wave function regarding them is not simple. Quantum numbers like spin are discontinuous, spin up or down, and the entanglement displays the necessity of the conservation of quantum numbers in a simple manner. That is the part where people try to use "entanglement" in practical applications, but my background does not extend to that. One thing I am sure of is that no information can be transferred by entanglement. The information should be already there in the knowledge of the mathematical form of the wavefunction, and the measurement by finding what one component is immediately knows the value for the entangled component by quantum number conservation.

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Entanglement is not necessarily equivalent to measurement, if the entanglement is reversible. Measurement has to do with an irreversible event, like photon absorption or emission.

Until an irreversible event occurs with X or Y, the entanglement of X with Y just results in the creation of an entangled, composite, XY wave function (and composite XY density matrix), but also results in the loss of the individual X and Y wave functions. However, a "reduced density matrix" for X and for Y still exists.

The XY wave function evolves via Schrodinger's Equation until an irreversible event occurs.

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