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Apart from the 'yes' as the first word in @Daniel's answer, I think the rest of his answer is correct. EPR claimed some 'spooky action at a distance', and that it proved QM was not true. Bell's theorem and inequalities, and the experiments carried out, proved that there was no such issue, that QM does not allow a local hidden variable explanation, by ...


0

Supposing that you know well the Bell test experiments with all its devices. The Bell theorem made a QM prediction about the correlations between entangled photons. This prediction is different than the realists one. Bell expected that the realists may not do better than 50% with a full photons detection. In fact, not-canonical-QM theorists know how to ...


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Yes - these experiments have been conducted, most famously by Aspect et al., but also by others, see Wikipedia. They all observed violations of Bell's inequalities - Our world is therefore not local-realistic in the sense of Einstein. An extension of Bell's inequalities by Legett (Legett inequalities) holds for non-local realistic theories. Their violation ...


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"Agreeing" to engage in a mutual activity at a predetermined time is not "ftl" . Not even close. That's simply a "coordinated simultaneous event". For it to truly be FTL the "clicking of the heels" would need to be observed BEFORE the stimulus that caused the clicking took place. In other words the other guy would have to SEE OR HEAR the clicks before the ...


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I'm assuming that you have a finite-dimensional base Hilbert space $\mathcal H_0$ and that you're building your full Hilbert space as $\mathcal H=\mathcal H_0\otimes \mathcal H_0$. In these conditions, the set of separable states has measure zero. (It gets a bit more complicated if you have $\mathcal H_0^{\otimes 4}$ and you're allowed to split it any way ...


5

The set of entangled states is open and dense in the space of all states (for a given system). In that sense, almost every state is entangled.


8

No, in fact, "most states" are entangled. (This is meant to be a heuristic; I freely admit this is probably a sticky thing to get into formally as far as randomly picking a state.) My intuition/reason for saying this is that there exist approximation methods which work by restricting themselves to a low-entanglement subspace, such as Matrix Product States (...


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I know from this talk by M Horodecki that entangled states are more abundant than separable states. Also see this paper on how separable states form a set of measure zero in pure state space. As for your argument, I think it can also be seen this way. $|\psi\rangle = |\psi_1\rangle \otimes|\psi_2\rangle$ can be viewed as a constraint on the structure of ...


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Entanglement is fundamental to our understanding of the behavior of matter. If you get rid of entanglement then matter must behave differently. Which would break the processes that keep your body working. Actually, entanglement is so deep in quantum mechanics that it's not clear how you could remove it without just throwing out the whole theory. It's a bit ...


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Entanglement manifests via correlations. If you can get rid of entanglement while keeping those correlations, I guess nothing will change in your life. So what is the question exactly? If it is, "do we know how to reduce quantum correlations to classical ones?" (ie. do we have a proper hidden variables theory), the answer is no (at this time, no such ...


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I will turn my comment to an answer, in reality answering your statement in the comments: Thus I am asking "what everyday processes require quantum entanglement rather than just classical correlation?" Classical probabilistic analysis depends on classical dynamics, the emergence of entropy from statistical mechanics is a good example. There have ...


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The question assumes that quantum entanglement actually happens the way it has been described by quantum mathematics. Which may or may not be true. All is not set yet. Leaving that aside - In any case, entanglement is not a law in itself, it is a phenomenon. It is a consequence of basic underlying laws at quantum level. For example, anti correlation of spin ...


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The canonical example for MPS (in fact, the first MPS ever) is the AKLT model (http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.59.799, https://projecteuclid.org/euclid.cmp/1104161001). The 2nd reference also discusses the 2D (=PEPS) version of the state. Another example of an exact MPS/PEPS model are (nearest-neighbor) RVB states (https://arxiv.org/...


0

I would like to get some help concerning the definition of information [in the context of sending information] Suppose Alice and Bob are playing a game. The communication game. The communication game goes as follows: A referee flips a coin, and tells Alice the result. (Alice and Bob apply some strategy X.) Elsewhere, Bob tells a second referee what he ...


3

There is something called quantum steering. The correlation between two EPR pairs means that if one pair is in some dynamic evolution due to some interaction that the other part of the pair will execute the same evolution. An example is with ESR/NMR for two charged spin particles in an entangled state. If one particle enters region A with a magnetic field it ...


2

Note that you can use the entanglement entropy to calculate the amount of entanglement in a bipartite pure state, but this is not a good measure for a general bipartite (mixed) state. In the general case there are several different entanglement measures currently used, which have certain desiderata: https://quantiki.org/wiki/axiomatic-approach. Invariance ...


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The answer is no: whether or not the state can be written as a product state does not depend on the basis. And you are precisely correct: there is indeed a basis-independent invariant that characterizes the entanglement. It is called the "entanglement spectrum": the eigenvalue spectrum of the reduced density matrix produced by taking the partial trace over ...


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No, the entanglement (yes/no) doesn't depend on the basis of the two subsystems, only on the way how the two subsystems are separated from one another. A non-entangled state is a state of the form $|j\rangle \otimes |\alpha\rangle$ for some states $|j\rangle,|\alpha\rangle$ of the two subsystems; all other states in the composite Hilbert space are entangled....


1

To add on to WillO's answer, I think the key in entanglement is not "which measurement happens first" or "which measurement affects the other", but rather that $|00\rangle$ and $11\rangle$ are the only possible outcomes! No matter what frame you switch to, you will NEVER get $|01\rangle$ or $|10\rangle$. Even if you consider the different frames in which ...


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The outcome is determined (probabilistically) by the state, and is either $|00\rangle$ or $11\rangle$ (assuming that's the observation you're making) equiprobably.


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First an important clarification about simultaneity you need to be aware of: In special relativity we learn that there is no such thing as two spatially separated events A and B happening 'at the same time', at least not in any absolute sense. If one inertial observer sees the events as simultaneous, another perfectly legitimate inertial observer sees A ...


0

The IQH state cannot be changed to a product state via local unitary transformation (ie cannot be smoothly deformed into a product state without phase transition), thus, according to the original definition of long-range-entanglement in http://arxiv.org/abs/1004.3835, IQH state is a long-range-entangled state (ie has topological order). Later Kitaev ...


2

When we create an entangled state in the lab, really what we are doing is creating a 'known' entangled state that we can then experiment with. As ACuriousMind said in the comment, most of the time things ARE entangled. What is entangled depends on whether the observer has interacted with it or not. If an observer interacts with a dynamic system and then ...


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No, not really. The amount of entanglement and the amount of energy in a state are completely independent: entanglement (together with discord) is a property of the state itself and its relationship to a bipartite (or multipartite) structure of the Hilbert space in which it lives, whereas energy is a joint property of the state and the system's Hamiltonian....


0

Teleportation and entanglement do not involve FTL communication of any kind. There is a local description of the evolution of any given quantum system in terms of its Heisenberg picture observables. The observables change only when the system changes by itself or through a local interaction with another system. Entanglement and teleportation can be ...



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