We discuss an effective simulation of quantum entanglement is presented using classical fields modulated with n pseudorandom phase sequences (PPSs) that constitute a n2^n-dimensional Hilbert space with a tensor product structure.
Is it reasonable？
If it is right, quantum entanglement is the unique property of quantum mechanics?
see http://arxiv.org/abs/1502.07002v2
http://arxiv.org/abs/1502.07002v2
Yes, quantum entanglement features can be present in classical fields, because the two mathematical properties underlying entanglement are the validity of the superposition principle and the existence of a bipartite (or multiparty) Hilbert space. These features are commonplace in classical electromagnetism where electric and magnetic fields obey the superposition principle and possess independent (e.g., polarization and spatial) degrees of freedom. For details see: http://arxiv.org/abs/1409.0213 "Classical entanglement: Oxymoron or resource?"
It is important, though, to make it clear that entanglement and nonlocality are different properties of a system, and only the latter seems to be an exclusive feature of the quantum world.
Doubt it, although I have to read your paper in depth. In a nutshell, quantum entanglement occurs because there is no role played by the spacelike separation between the variables of a multi-variable wave function obeying a valid Schrödinger equation. If you impact one of the variables, the other variables must then react instantly so that the corresponding Schrödinger not be violated, and it cannot be violated if decoherence has not set in.
To transpose this into the classical arena, you'd have to replace Schrödinger's by its classical equivalent : a standing wave function. Now do this experiment: build a standing wave on a rope - for instance affix one end of the rope to a wall - (where amplitude is thus nil) - and move the other end up and down - (at peak amplitude): a stationary system of peaks and troughs will form. Now instantly , while still imparting the same up and down motion, cut a bit of length off the rope.
In the QM case the rope would instantly settle into a new scheme of peaks and troughs with a different period length and amplitude scheme. It does not in the classical case, because signal is conveyed by the rope and its speed is finite
Yes, quantum entanglement features can be present in classical fields, because the two mathematical properties underlying entanglement are the validity of the superposition principle and the existence of a bipartite (or multiparty) Hilbert space. These features are commonplace in classical electromagnetism where electric and magnetic fields obey the superposition principle and possess independent (e.g., polarization and spatial) degrees of freedom. For details see: http://arxiv.org/abs/1409.0213 "Classical entanglement: Oxymoron or resource?"
It is important, though, to make it clear that entanglement and nonlocality are different properties of a system, and only the latter seems to be an exclusive feature of the quantum world.
Bell's inequality can be violated by classically entangled systems, see, e.g., the very good article Phys. Rev. A 82, 033833 (2010) - "Bell-like inequality for the spin-orbit separability of a laser beam", http://journals.aps.org/pra/abstract/10.1103/PhysRevA.82.033833. The point here, again, is that Bell's ineqaulity may be considered either as an entaglement witness (and, therefore, are violated by classical entanglement), or as nonlocality witness, and in this case they cannot be violated by classical entanglement.
Apparently, classical field have superposition similar to quantum mechinics, such as polarization of light field.
All bell-type correlation demostrate that you can at same time obtain correlated measurement results of two quantum particles with space-like separations (including Zbinden, H.; Gisin, N., et al, "Testing the speed of ‘spooky action at a distance". Nature, 2008. 454.) ) . The key is where the randomness of measurement results comes from. The randomness might not be derived from the measurement process but from some internal mechanism of quantum particles.
In following paper, it shows my point of view.
http://arxiv.org/abs/1502.06347
Dear Akira Kanda and Jian Fu,
I would like to add a few words to this discussion. I think that it is important to understand what we mean with "nonlocality". To this end, I would suggest to read Sec. 8 of the beautiful and clear article by Prof. B-G. Englert "On quantum theory", Eur. Phys. J. D (2013) 67:238. Quoting from there: [Quantum theory is a local theory in exactly the same sense as all other physical theories: All interactions come about by local couplings; a continuity equation states that probability is locally conserved; energy, momentum, angular momentum, and other properties are transferred between particles by highly localized scattering events, and so forth. And just like the other local theories do, quantum theory predicts nonlocal correlations that originate in local processes.]
So, what we usually mean with "nonlocality"? We all know that correlations between distant and no-signalling physical systems are possible (and, actually, quite common) in both classical and quantum systems: I denote such correlations as "nonlocality". What distinguishes classical from quantum nonlocality is that in the former the correlations between the systems are established "a priori", namely before the two systems are set apart, by the act of preparation of the state. Vice versa, in quantum mechanics such correlations are established "a posteriori" by the act of measurement (as opposed to preparation) of the state, after the two system have been spatially separated.
Dear Prof. Andrea Aiello
I agree your viewpoint!
I understand "a posteriori" of quantum mechanics is related with unitary operates thita1 and thita2 in correlation measurement. And in our simulation, the results also demostrate the posteriori. Actually, our states are establed "a priori" relationship by using PPS. In our scheme, the "priori" relationship is compatible the posteriori of quantum mechanics. I believe quantum entanglement undercover hidden variables must relate to phases. I strongly doubt that the coincidence counting method in quantum correlation measurement only crop the beneficial evidences for quantum entanglement.
Dear Akira,
I am sorry to contradict you, but quantum mechanics does not predict superluminal particle propagation neither the absence of "coarse graining" trajectories, as the ones observed in a bubble chamber. The correct application of the basic principles of quantum mechanics had always yielded to predictions in agreement with the experimental findings so far. So, there are NO DOUBTS about its correctness at the level of energies we tested it. However, if one wants to argue that quantum mechanics does not satisfy our "classical" intuition and sense of logic, he or her is welcome; certainly the philosophical foundations of quantum mechanics are prone to generate intriguing questions. However, physics is not philosophy.
In agreement with Andrea that quantum entanglement features can be present in classical fields. It is to be noted that while non-locality (linked to the violation of Bell inequality of any form and considered to arise from complementarity or the impossibility of simultaneous joint measurements of observables) is a feature which reflects entanglement, the converse is not true. Thus not all entangled states reveal non-local features. Non-locality is a sufficient feature, but not necessary to reveal entanglement (see ref)
ref: F. Buscemi, Phys. Rev. Lett. 108, 200401 (2012).
This paper "Effective Simulation of Quantum Entanglement using Classical Fields Modulated with Pseudorandom Phase Sequences" has been published on ScienceOpen Research. Warmly welcome peer review! Thank you very much!
https://www.scienceopen.com/document/vid/b3ef92df-4b57-4c14-97ae-7ada2677cf8f?9
Andrea Aiello has given a good answer. I would like to remind that quantum entanglement is only a necessary condition for non locality, not a sufficient one. Moreover quantum non locality is not limited to entanglement; see for example Aharonov-Bohm effect or delayed choice experiments. Other typical properties of quantum mechanics are: contextuality, dualism, complementary and indeterminism.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics
- Quantum Mechanics