Hot answers tagged entanglement
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Entanglement is being presented as an "active link" only because most people - including authors of popular (and sometimes even unpopular, using the very words of Sidney Coleman) books and articles - don't understand quantum mechanics. And they don't understand quantum mechanics because they don't want to believe that it is fundamentally correct: they always ...
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I wish to complete @Luboš Motl's answer, to which I agree. My point is on why people continue to make this mistake of an active link. This mistake is connected with one of the most interesting properties of quantum mechanics, Bell's theorem. One can argue that any physical theory is an hidden variable theory, the hidden variable being the description of the ...
25
I understand your confusion, but here's why people often feel that quantum entanglement is rather strange. Let's first consider the following statement you make:
2 things have some properties set in correlation to each other at the point of entanglement, they are separated, measured, and found to have these properties
A classical (non-quantum) version ...
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It's not possible to communicate faster than light using entangled states. All you get out of entanglement is a correlation between the values of two measurements.; the entanglement doesn't allow you to influence the value measured at another location in a non-causal way. In other words, the correlation only becomes evident after combining the results from ...
14
First of all, it is very important to note that quantum entanglement is not a spooky action-at-a-distance as Einstein once called it! It is a strong correlation of measurements that is stronger than any classical correlation could ever be. This has been experimentally verified by the so-called violation of Bell's inequalities.
Second, quantum entanglement ...
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A short summary of the relation between MPS/PEPS and ground states local Hamiltonians:
First the direction from MPS/PEPS to Hamiltonians:
Every MPS/PEPS naturally appears as the exact ground state of a frustration free local Hamiltonian. ("parent Hamiltonian")
For generic MPS/PEPS, this ground state will be unique.
There is a number of cases beyond the ...
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The standard test for whether two things are really entangled with one another in the spooky-action-at-a-distance sense of the EPR picture is to see whether measurements of the states of the two particles violate one of the Bell inequalities, meaning that the correlation between the states is stronger than can be explained by any local hidden variable ...
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The original goal of the EPR paper was to show that quantum mechanics is incomplete. Hence, that extra variables have to be added to complete it, contrary to what Cedric claims. The goal of EPR is to show that either nature is non-local (and thus in conflict with SR) either quantum mechanics is incomplete. Since Einstein was not ready to abandon locality and ...
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From what I understand, entanglement isn't destroyed, it is only obscured by subsequent interactions with the environment.
Depends on how you view it. There is an explanation of quantum measurement (called decoherence) in which this is true. I will not be using that explanation in this post because it's unnecessarily complicated.
This will have some ...
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To answer this kind of question properly, it's important to clarify the foundational issues of why SR forbids superluminal speeds and what kind of superluminal speeds it forbids. There are several independent arguments of this kind that tell us several different things.
Superluminal transmission of information would violate causality, since it would allow ...
10
Just a nice analogue Prof. Jürgen Audretsch told me once:
Imagine at home you put one glove in your coat without looking (and noticing it's only one of the two). After exiting the train you notice it's cold and you pull out that single glove. At this very instant you know it's either the left or the right glove, and you therefore know which one is left ...
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Collapsing an entangled pair occurs instantaneously but can never be used to transmit information faster than light. If you have an entangled pair of particles, A and B, making a measurement on some entangled property of A will give you a random result and B will have the complementary result. The key point is that you have no control over the state of A, ...
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Rather than repeat some very good standard answers, I want to discuss this issue from the perspective as to why classical systems should be viewed as strange.
If we accept quantum mechanics as being fundamental, then in some sense we shouldn't really find things like entanglement to be strange at all. As pointed out by the answer given by joshphysics, as ...
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No, there is no retrocausal causation in the delayed choice entanglement swapping experiment (or any other experiment or process in the Universe, for that matter), see
http://motls.blogspot.com/2012/03/has-anton-zeilinger-created-time.html
for a detailed explanation. Correlations between Alice, Bob, and Victor's outcomes may obviously be verified only ...
9
Aram's answer seems perfect, but since you are also asking about the case for higher dimensional systems, let me add that there is a simply way to get somewhat non-trivial upper and lower bounds on $C(j_S,j_L)$. As a lower bound, you can simply synthesize an arbitrary gate which implements communication between the quantum systems (for an explicit algorithm ...
8
Entanglement is a quantum correlation between two (or many) objects - a correlation means that these two objects' properties are not independent of each other - which was created in the objects' common past when they were close to one another i.e. when they were two parts of the same physical system.
Quantum mechanics changes the character of possible ...
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Well, the problem in that paradox is that yes, one of the parties will measure the entangled particle to get the wave function collapsed and yes it will collapse for the other party. However, the other party will still have to measure the thing to learn what it is or has to wait for the initial party to send them a message telling what the wave function has ...
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Dear sb1, the assumptions implicitly contained in your question are upside down. Exactly the fact that the degrees of freedom of the Universe are becoming increasingly entangled means that we cannot observe the quantum phenomena in practice.
The entanglement that emerges after a relatively short time is the entanglement among a huge number of degrees of ...
8
No. What you describe is not what is meant by quantum entanglement. What you describe would allow instantaneous communication across large distances which would allow violations of causality and would violate special relativity.
Quantum entanglement occurs when you prepare two particles such that one is spin up and the other is spin down, but you don't ...
8
In quantum mechanics, two observables that cannot be simultaneously determined are said to be non-commuting. This means that if you write down the commutation relation for them, it turns out to be non-zero. A commutation relation for any two operators $A$ and $B$ is just the following $$[A, B] = AB - BA$$ If they commute, it's equal to zero. For ...
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This right description of multiparticle states via tensor product spaces may have been surprising for folks like Schrödinger and from the viewpoint of "wave mechanics", but it has been incorporated from the very beginning in "matrix mechanics", Heisenberg's and pals' approach to quantum mechanics.
After all, the wave functions for a single particle in 3 ...
7
Dear Gunther, a partial trace contains all the information about possible predictions made for the subsystem that you haven't traced over. It's trivial to see why.
First, take the whole system A+B. They may be entangled but we're only interested in future measurements of A. If the description for A+B is a pure state $|\psi\rangle$, then define
$$\rho = ...
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If a system S is composed of two subsystems A and B, then a state of S is a vector $$|\Psi\rangle \in H_A\otimes H_B$$ Tracing over the "B degrees of freedom" allows you to define the reduced density matrix $\rho_A$ The entanglement entropy is defined as$$-Tr(\rho_Aln\rho_A)$$
I believe that the entanglement spectrum just refers to the spectrum of ...
7
I think there are two sides to this question:
1) Why can we often treat systems with which our measuring devices are entangled as classical systems? This is explained by decoherence as pointed out in John Rennie's answer.
2) Why can we describe some systems in a lab as undergoing unitary evolution of their wavefunctions as prescribed by Schrodinger's ...
7
The normal state of subsystem is entangled, as follows from the Schroedinger equation, which turns a separable state immediately into an entangled state if there is some interaction.
The state of a subsystem is obtained from the state of the universe by tracing out all other degrees of freedom. This leaves a density matrix, which is a perfectly good state ...
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This is a typical trade-off between the position properties of the purple electron and its wave properties.
If the orange electron is sufficiently far so that it doesn't influence the purple electron much, everything will continue as before: the purple electron will produce an interference pattern while the orange one will draw one point on the photographic ...
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