Entanglement for identical particles doesn't follow textbook rules

(Left) A comparison of entanglement for nonidentical particles (red solid line) with identical bosons (blue dotted line) and identical fermions (orange dashed line). (Right) Density plot of entanglement for identical bosons, which—unlike nonidentical particles—depends on particle overlap. Credit: Lo Franco and Compagno. ©2016 Nature Scientific Reports

(Phys.org)—In quantum entanglement, two particles are correlated in such a way that any action on one of them affects the other even when they are far apart. The traditional methods of measuring the degree of quantum entanglement were originally developed for nonidentical particles, such as between an electron and a proton, or two atoms of different types.

Unfortunately, these methods do not work very well when applied to identical particles, such as two electrons or two helium atoms, since such particles are indistinguishable. The traditional methods often give false positives for entanglement between identical particles, claiming that they are entangled even when it's clear that they are not.

Consequently, there is no general method for measuring the degree of entanglement between identical particles, although over the past several years physicists have made many attempts at developing such a method. However, these proposals often contradict the well-established methods, with some going as far as to redefine the very notion of entanglement.

Now in a new paper published in Nature Scientific Reports, physicists Rosario Lo Franco and Giuseppe Compagno at the University of Palermo in Italy have developed a method for measuring entanglement between identical particles that uses the same fundamental concepts as those used by the well-established methods for measuring entanglement between nonidentical particles.

In their paper, Lo Franco and Compagno propose that the root of the problem (why the traditional methods work so well for nonidentical particles but not for identical ones) is the general convention of labeling identical particles to make them appear nonidentical. Labeling can be done by, for example, by assigning a number to each particle.

"In quantum theory, identical particles are made nonidentical by naming them with unphysical labels," Lo Franco told Phys.org. "This procedure works well in the usual practice, except when correlation properties, like entanglement, for such systems are considered."

By doing away with the labels altogether, Lo Franco and Compagno could open a new avenue for investigating how indistinguishability impacts the degree of entanglement.

"A delicate yet strong aspect of our work is that it somehow defies some common beliefs and prejudices about this decades-long debated issue of the entanglement of quantum indistinguishable particles," Lo Franco said. "We show that identical particles can be treated without name labels, in contrast with the very usual textbook practice, maintaining a particle-based approach in terms of states. This enables the study of entanglement by means of the standard notions of entanglement theory for distinguishable particles."

The new approach finally provides an answer to the previously unanswerable yet basic question of whether or not two identical particles are entangled. The results reveal that, if two identical particles with opposite "pseudospins" (a property that does not make the particles different) are brought so close together that they begin to overlap each other in space, then they will become entangled. This theoretical result can help explain a recent experimental observation in which entanglement was generated simply by moving two ultracold rubidium atoms with opposite spins into the same optical tweezer.

The results also show that the degree of entanglement between identical particles depends on the degree of particle overlap, where particles that occupy the same exact space are maximally entangled. This relation between entanglement and overlap is unique to identical particles, as the entanglement of nonidentical particles does not fundamentally depend on particles occupying the same space.

In addition, the results show that the degree of entanglement between identical particles is always greater than that of nonidentical particles. This finding suggests that identical particles may be more efficient than nonidentical ones at becoming entangled, which has important implications for designing entanglement-based quantum information technologies.

Since overlap is a critical feature of identical particle entanglement, the results could lead to new experiments that use quantum correlations for quantum information tasks that are implemented in systems in which particle overlap is important. These systems include Bose-Einstein condensates, quantum dots, superconducting circuits, photons in waveguides, and aggregates of biological matter.

"Our work foundationally contributes to clarifying the relation between and the identity of particles," Compagno said. "It also motivates studies that involve correlations other than . These areas have already been experiencing a huge amount of attention with nonidentical particles, but now we can investigate these correlations in the context of identical particles as well."

Explore further

A way to study entanglement entropy between multi-body systems

More information: Rosario Lo Franco and Giuseppe Compagno. "Quantum entanglement of identical particles by standard information-theoretic notions." Nature Scientific Reports. http://www.nature.com/articles/srep20603. On Arxiv: http://arxiv.org/abs/1511.03445
Journal information: Scientific Reports , arXiv

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Feb 09, 2016
"In quantum entanglement, two particles are correlated in such a way that any action on one of them affects the other even when they are far apart." - Writer, you must be joking? It doesn't 'affect' the other particle, it merely predicts the state of the other particle if we measure the state of this one. Else, the information exchange would be possible, and it is not possible. Everyone with undergrad in physics should know this.
Back to school, tech writer Lisa Zyga, my girl.
Else, very interesting research. Like it

Feb 09, 2016
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Feb 09, 2016
+promile I have an orange and a banana, I put one in box 1 and another in box 2. You then take box 2 to somewhere very far away from me. You open box 2 to reveal the banana. This means that I have the orange in box 1. At no point have you travelled superliminally to interfere with my box, it is literally the only possibility that I have the orange given that you have the banana. The only thing you have 'affected' is your knowledge of the combined system.

Feb 09, 2016
Actually, NoStrings, you're not quite correct either. If it "merely predicts the state" then we couldn't exchange information either, because it doesn't carry any new information. The bigger picture is that entanglement means that there is a state encoded in the *system* of two particles that cannot be gleaned from either one particle alone.

The classic example is creating particles with entangled spin up and down. After creating them, Alice may flip one "upside-down," rotate it along the X or Y axis, or leave it unchanged, thus having 4 possible states. Bob measures his particle, but doesn't know which rotation Alice performed. Alice measures hers, tells Bob her results, and Bob can use that answer to determine which rotation Alice performed.

The catch is that the relationship changes if the particles have an explicit state prior to being measured (no superposition of states) AND that state information is transmitted at c or slower. Experiments don't show such a relationship

Feb 09, 2016
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Feb 09, 2016
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Feb 09, 2016
Entanglement is not restricted to a single point in time - when it was decided to tag each particle. The future trajectory not being established yet, there is a non-vanishing probability for other trajectories, and therefore entanglement in time as well.

Asimov was humorously prescient with his joking thiotimoline paper.

Feb 09, 2016
"In quantum theory, identical particles are made nonidentical by naming them with unphysical labels,"

There is much confusion here. On the presumption that there are two entangled particles, they were never *identical* in the strong sense (as Mark Twain is to Sam Clemens). From the rest of the article, I would assume they are two tokens of a particle type -- e.g. two electrons. But labels don't change electrons into non-electrons. They are just linguistic devices that allow us to refer (or talk about) either particle individually. So is the claim that we cannot even do that? Because that sounds a lot like saying that entangled particles really are identical in the strong sense -- that there is just one particle in two places.

Feb 10, 2016
You open box 2 to reveal the banana. This means that I have the orange in box 1

That's a hidden variable theory : that the box contains a banana or an orange all the way to you. This is not the case with entanglement. The contents of the box is not determined until it is opened because the property of the object being banana or orange is entangled.

It's more like flipping two coins and finding that one always lands on heads when the other is tails, even though you flip them individually and the flip is random. There's a bit more to it, but the point is that the property being measured is not something that is, but something that can be, like the banana pointing west or east when you open the box.

Feb 10, 2016
Because that sounds a lot like saying that entangled particles really are identical in the strong sense -- that there is just one particle in two places.

The sensible interpretation of the situation is that you haven't got a particle at all until you measure one to be there, so it's pointless to put an identity on something that doesn't exist.

The thing or property that is being entangled is due to there not being enough information in the system to define all properties of the system, and that information is added from the outside. The particle, or the history of there having been one, only appears in relation to what it interacts with.

So e.g. if we split a spin-0 particle into two spin-½ particles, one pointing up and one down, we haven't yet added the information about which of them went to Alice and which went to Bob. When we ask Bob and Alice which version they found, we add that information by forcing the system to become self-consistent.

Feb 10, 2016
Mind you, in the above situation, we are still in superposition about which particle went to Alice and Bob - the information that one definitely got one or the other still doesn't exist - only that one got the opposite of the other.

But just like Shrödiger's cat, we don't percieve ourselves to be in two contradictory states. The states percieve only themselves.

If someone else came along to add some information that is consistent with the fact that Alice got spin -½ and Bob got spin +½ then that would collapse the superposition.

Having an entangled particle is like trying to follow a photon through the double slit experiment. There isn't enough information to say which way it went, so it goes both ways, and once you try to measure which way it went you automatically add something that defines exactly where it went and that changes the outcome.

Feb 10, 2016
@promile: ...The entanglement provides, that this energy affects the states of both pieces of fruit at the same moment.
I agree with this explanation. But I would add one more thing about the energy requirements. The energy to measure one fruit (affecting it) should be double to measure both, affecting the state of both. But in this case , we only need half of it. This also indicates that they have to be a unique fruit up to the moment of measurement, not "one fruit affecting the other" in any way.

Feb 13, 2016
we're dealing with things without the energy necessary to express unique states despite ambient energy flux. only upon measuring do we define the state. that's not to say proclivities don't exist before the measurement -- it's not strictly R & L gloves in discrete boxes. nevertheless spin is 'motivated' by the environment's own reciprocal version of the state.

Feb 14, 2016
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Feb 14, 2016
If I avoid classifying electrons as particles (or waves) then consider these identities as expressions of an underlying electric (or magnetic) field, then observations of less than intuitive properties can be rationalised.

Balloons and water analogies are likely to upset some but it's all I got at the moment so here goes ..

Take a balloon and using a fine needle jab some holes. Then fill the balloon with water. On the balloon surface little beads or droplets of water can be seen. These water particles can be observed examined and tested but until you realise that they are expressions of the underlying volume of water in the balloon, you will have difficulty understanding how they are interconnected.

( Raising shields Captain - IMO ).

Feb 14, 2016
I could look at the morning dew and examine the drops of water. Test the dew drops. Smash them together. Whatever. However, until I know that dew drops are expressed from the surrounding air, I'd be misunderstanding their nature.

Feb 14, 2016
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Feb 14, 2016
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Feb 17, 2016
I can't wait!

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