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So I know that two particles can be entangled in a quantum way, but is it possible that more than two particles be entangled in a quantum way? Most descriptions provide with two-particles cases, so I wonder. (It's hard to think of three particles entangled in spin, or so.)

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  • $\begingroup$ nature has no problems. think of crystals. $\endgroup$ – anna v Feb 19 '13 at 8:19
  • $\begingroup$ No answer so far seems to address the well known phenomenon of monogamy of entanglement. If A is very entangled with B it cannot be highly entangled with C. In particular if A is maximally entangled with B it cannot be entangled with C. This said it is easy to construct states where all bipartitions are entangled. $\endgroup$ – lcv Dec 16 '19 at 10:53
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Yes, you can have as many entangled particles as you want. It might be rather cumbersome to achieve it but it can in principle be done. Multipartite entangled states actually lie at heart of a special type of quantum computation, called measurement-based quantum computation. Here, you start from a large entangled state of many parties (usually called cluster state) and by performing certain measurements on certain parties of the state achieve required state of the rest of the system. You might want to google it up, there is quite a lot of literature on this topic.

The multipartite entangled states, however have to major drawbacks - as I already said, they are not always easy to prepare, and secondly, it quickly becomes difficult to classify their entanglement. Let me illustrate this on a system of two and three qubits.

With two qubits, it is easy to decide whether a given system is entangled or not - the positivity of the partial trace is a necessary and sufficient condition for separability. But with three qubits (let's denote them by A, B and C) things start to get a little messy. You can consider three bipartitions of the whole system, A|BC, B|CA, C|AB, and look at their separability properties. Now, it may happen that the state will be separable with respect to the A|BC partitioning but not to the C|AB partition. (I am not completely sure about this, but this is the way it works for continuous-variable Gaussian states). You might even find that all three partial traces are positive but you won't be able to find a separable state of all three systems (such states are called bound entangled). So in principle, you can have states completely inseparable, separable with respect to one or two bipartitions, states separable with respect to all three bipartitions but not completely separable, and fully separable states.

And now, imagine going to four qubits. Now you can separate the system in 2+2 or 1+3 subsystems and the possibilities grow. So it becomes almost impossible to classify the entanglement of the given state. And entanglement quantification of such complex systems is even more problematic.

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    $\begingroup$ Ondrej Crnotik There is also a possibility that the entire universe was created in an entangled quantum state. $\endgroup$ – JKL Feb 20 '13 at 16:54
  • $\begingroup$ There is some confusion here. Bound entangled states exist also for bipartite systems. The overall Hilbert space dimension need to be greater than 6 though. $\endgroup$ – lcv Dec 16 '19 at 10:47
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Yes and the highest record is 3000 quantum entangled particles https://www.livescience.com/50280-record-3000-atoms-entangled.html

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I want to add this answer, since the above question is pointed out as a duplicate for a recent one. My answer is , as I have stated in a comment above, that all quantum mechanical states are entangled, and since in theoretical principle, a single wave function can describe the universe, the answer to the title should be automatically yes.

Reading these answers I realize that the general physicist and the quantum-computation-aligned physicist give a different physics definition for entanglement. They mean in quantum computers, if in the laboratory one could control a sample so that the desired quantum numbers are entangled, in effect "know the entanglement" by construction. This is the way the question is answered and accepted, so I suppose the question was from a quantum computing framework.

In a general definition of the word entangle in the webster dictionry though

a: to wrap or twist together : INTERWEAVE

this is the closest to the mathematicl condition.

Entangle as it is used in physics should have new entries.

All variables in a quantum mechanical function are entangled, i.e. the value of one depends through the differential equations on the value of the others and are consistent with the above dictionary definition. A new entry should be given for quantum computing.

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  • $\begingroup$ I strongly disagree. In physics the word entanglement has a precise meaning which is the 'information theoretic' one alluded in other answers. If other branches of physics are not familiar with that meaning you should not try to substitute the common English meaning for that word. The energy is very precise thing that is measured in Joules even if my field is not thermodynamics. In Chinese medicine (and everyday life) energy is a different thing (we 'feel energized'). Note that the word entanglement was chosen by Schroedinger to mean precisely what is meant in other answers. $\endgroup$ – lcv Dec 16 '19 at 11:02
  • $\begingroup$ @lcv that is why I ask for a new entry to the meaning of the word. Even in every day meanings there are often more options. How much so when the word is being used in a mathematically concise way in quantum computing. Do not forget that this is a site for general physics questions, all sorts of physics, not just quantum computing. . Why would you disagree to having a separate definition for quantum computing? In principle everything is entangled " in a quantum way" . To know exactly the entanglement is a step further in quantum mechanics description.. $\endgroup$ – anna v Dec 16 '19 at 11:38
  • $\begingroup$ First it's not about quantum computing. As I said the word entanglement (or rather the german Verschränkung) was used by Schroedinger in 1935 to designate what we mean today. Would you like the word 'energy' to have a different meaning in thermodynamics and in fluid dynamics? Of course the word energy had a meaning in English (and in every language) long before Carnot, Joule, and so on. But now in physics we use it with a very specific meaning. $\endgroup$ – lcv Dec 16 '19 at 12:15
  • $\begingroup$ @lcv "physics we use it with a very specific meaning" can yougive me a link for this very specific meaning? The answer by pankajdoharey which has got 3 updvotes, illustrates what I mean as difference between physicists "Yes and the highest record is 3000 quantum entangled particles" . When a crystal has ~$10^{23}$ $\endgroup$ – anna v Dec 16 '19 at 12:55
  • $\begingroup$ A quantum state is called entangled if it cannot be written as a separable state i.e. in the form $ \rho = \sum_j p_j \rho_j^A \otimes \rho_j^B$. If there is more than one non-zero $p_j$ such a state is also called classically correlated because any (bipartite) classical state can be written in this way. See en.m.wikipedia.org/wiki/Quantum_entanglement. Regarding crystals: can you prove (experimentally) that any bipartition is entangled? To tell the truth there are some results in this direction but this is another story. $\endgroup$ – lcv Dec 16 '19 at 14:12

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