Why is the distance in non-local entanglement for teleportation limited by time

Question

In a recent paper, researchers described a system that can teleport a quantum state without the need for the entangled particles to actually "meet" each other.

I'm reading, in particular,

Traveling without moving: Quantum communication scheme transfers quantum states without transmitting physical particles (Stuart Mason, phys.org).

The author states that (emphasis mine)

scientists in China at Harbin Institute of Technology, Yanbian University and Changchun University demonstrated what is known as a counterfactual approach in which quantum information can be transferred between two distant participants without sending any physical particles between them. The researchers accomplished this by entangling two nonlocal qubits with each other without interaction – meaning that the present scheme can transport an unknown qubit in a nondeterministic manner without prior entanglement sharing or classical communication between the participants. Moreover, the scientists state that their approach provides a new method for creating entanglement that allows two qubits to be entangled without interaction between them.

[...]

Theoretically," Zhang acknowledges, "a galactic or intergalactic internet may be possible based on the present scheme, which would require a so-called long-arm intra- or intergalactic interferometer and a quantum obstructing object with very long coherent time. Obviously, however, it's currently unpractical to construct a long-arm interferometer, and there is no known quantum state with such a very long coherent time.

I'm not sure what they're talking about with the long-arm interferometer, but if they can really transport the quantum information without the entangled particles meeting, then why would how long the coherence can be maintained determine the "distance", since "nothing" is traveling between the two separate locations?

Answer 1

Not really.

It is indeed perfectly possible to entangle two particles A and B without using direct interactions between them, the easiest example being to entangle A with some ancilla system C, carry C over to B, and then swap the states of B and C, which will transfer the A-C entanglement onto the A-B pair.

This is of course not magical at all, and the approach in that paper is not very different from this. In particular, their approach still requires some ancillary system to travel between A and B, or for A and B to send one ancillary system each to a halfway location. Zhang's claim of an "intergalactic entangled internet" cannot be achieved without reliable intergalactic transport of photons. For more details, see Zhang et al.'s actual paper,

Counterfactual quantum-information transfer without transmitting any physical particles. Q.Guo et al. Sci. Rep. 5, 8416 (2015).

It's open access and the figures clearly show photons propagating (repeatedly) between Alice and Bob.

This is not to say, however, that the scheme in question isn't weird. The way this "counterfactual entanglement" works is roughly as follows:

• Start with two excited systems in separate locations (say, two single ions in separate ion traps, a few meters apart), and allow them to decay and emit a photon.
• Collect the photons and put them in optical fibres.
• Bring the optical fibres together and connect them to the input ports of a 50:50 beam splitter.
• Put single-photon detectors on the output ports of the beam splitter.

If you detect a single click on only one of the detectors, you know that one of the atoms has decayed to the ground state $|g⟩$ and that the other is still in the entangled state $|e⟩$. However, because there is a beam splitter between the detector and the atoms, you cannot know which is which. Even better, as it turns out, is that if you go through the math for it, the ions end up being entangled with each other, despite never having "met". So this is in some sense magical, or at least it's better than the first scheme I mentioned.

It's important to note, however, that even here the statement that both ions are entangled looks a lot stronger than it actually is. In particular, you cannot use entanglement to communicate, either faster or slower than light. The only 'weird' thing that entanglement allows you to do is to perform simultaneous measurements whose outputs will exhibit bizarre sorts of nonlocal correlations (i.e. the correlations are stronger than would be possible using hidden local variables, but not strong enough to signal). If you do that, though, in the end you are only making a complicated statement about the correlations between measurements of the two ions and the photons they emitted, which is much more mundane than what you started with.