Timeline for Is there a quantitative relation between the correlations at spacelike intervals possible in quantum field theory vs classical field theory?
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| Oct 14, 2016 at 14:57 | comment | added | ACuriousMind♦ | @VineethBhaskara Please don't write answers that reply to comments. In this case, I have converted your answer into a comment, but generally you'll have to reach 50 reputation to comment on other people's posts. | |
| Oct 14, 2016 at 14:45 | comment | added | Vineeth Bhaskara | @Girish: Concurrence is a good measure even for multi-qudit pure states. This has been extended to pure states of arbitrary dimensions (aka multi-qudit pure states) in a very intuitive way by looking at the geometry of the tensor products with increasing dimensionality. A very clear and pedagogic explanation to reach the generalization from the basic notion of separability may be found here: arXiv:1607.00164 (2016). | |
| Aug 17, 2016 at 8:39 | history | bounty ended | Girish Kulkarni | ||
| Aug 16, 2016 at 15:28 | vote | accept | Girish Kulkarni | ||
| Aug 15, 2016 at 6:54 | comment | added | Girish Kulkarni | Let us continue this discussion in chat. | |
| Aug 14, 2016 at 11:45 | comment | added | flippiefanus | Yes, this is what I said: HBT correlations can be explained classically. However, I've noticed that there has been work done by Mandel and Glauber on HBT in the quantum context. | |
| Aug 14, 2016 at 7:11 | comment | added | Girish Kulkarni | So as far as the field is concerned, a perfectly classical picture suffices to explain the HBT experiment. Let me see if I can cite a reference that supports my claim. | |
| Aug 14, 2016 at 7:09 | comment | added | Girish Kulkarni | I am not sure I agree. The HBT correlations can be calculated from a P-function which is a well-behaved positive-semidefinite probability distribution. The measurement can be modeled in a semiclassical picture by considering the field as a classical electromagnetic field, and the device as a quantum two-level system. Under the weak field approximation, we can use time-dependent perturbation theory to calculate the detection probabilities at the two detectors. | |
| Aug 14, 2016 at 7:00 | comment | added | flippiefanus | @Girish: I quickly had to look up the HBT correlations. Although they can be explained classically there are also quantum implications. When it comes to photon antibunching one makes a local measurement. For that one would need one photon-number-resolving detector (otherwise how do you know you've detected two photons instead of just one). That would make the measurement intrinsically quantum mechanical. As a result one cannot really interpret the result classically. | |
| Aug 14, 2016 at 6:44 | comment | added | Girish Kulkarni | So since nonlocal entanglement is impossible for classical fields, the classical four-point correlation functions can at best quantify HBT-type correlations. In fact, photon antibunching which leads to $|g_{2}(0)|<1$ is a quintessentially non-classical feature. In fact $|g_{2}(\tau)\geq 1\,\,\forall \tau$ for classical fields, while $g_{2}(\tau)\geq 0$ for a general quantum field. So that is one instance where the range of accessible values for the four-point correlation function is clearly distinct for classical and quantum fields. | |
| Aug 14, 2016 at 6:27 | comment | added | flippiefanus | @Girish (second comment): Unfortunately, the answer (as far as I understand) is no. For the classical entanglement, the correlation is actually still a two-point function, but which contains two degrees of freedom for each field: $\langle \phi_{m,p}^* \phi_{n,q} \rangle$. The four-point function in classical fields cannot give nonlocal entanglement information, even though it can show some correlations as in the Hanbury-Brown-Twist type experiments. | |
| Aug 14, 2016 at 6:22 | comment | added | flippiefanus | @Girish (first comment): Yes that's correct. In my answer I only consider the bipartite qubit case. The situation becomes more complicated with more particles or higher dimensions. For entanglement among more than two particles one would need a corresponding higher order correlation function (n-point function). If you stay with two particles but consider higher dimensions then you would still need a 4-point function, but the dimensions of your density matrix would increase. | |
| Aug 14, 2016 at 6:06 | comment | added | Girish Kulkarni | So your point that four-point correlation functions quantify the entanglement is well-taken. But then one could argue that four-point correlation functions can be computed even for a completely classical field. The question then remains: are four-point correlation functions for classical fields allowed to take the entire range of values accessible for quantum fields? | |
| Aug 14, 2016 at 5:58 | comment | added | Girish Kulkarni | But the four-point correlation function contains information about the entanglement in a two-particle system. For instance, the visibility of the interference fringes in the coincidence count rate (four point function) of photon pairs produced from parametric downconversion is a measure of two-particle entanglement. Also, concurrence is a good measure of entanglement only for two-qubit states. For multipartite entanglement, there is no universally accepted robust measure. | |
| Aug 14, 2016 at 4:43 | history | answered | flippiefanus | CC BY-SA 3.0 |