Quantum energy teleportation without a limit of distance

Quantum energy teleportation (QET) is, from the operational viewpoint of distant protocol users, energy transportation via local operations and classical communication. QET has various links to fundamental research fields including black-hole physics, the quantum theory of Maxwell's demon, and quantum entanglement in condensed-matter physics. However, the energy that has been extracted using a previous QET protocol is limited by the distance between two protocol users; the upper bound of the energy being inversely proportional to the distance. In this paper, we prove that introducing squeezed vacuum states with local vacuum regions between the two protocol users overcomes this limitation, allowing energy teleportation over practical distances.

Figure 1

Schematic diagram of (a) vacuum-state quantum energy teleportation (QET) protocol and (b) long-distance squeezed-state QET.

Figure 2

Schematic showing abrupt expansion of the space where quantum fluctuation of the field becomes severely stretched. The upper figure depicts quantum fluctuation in the vacuum state before the expansion, while the lower figure depicts the stretched quantum fluctuation, which can be described by the modified mode function $v_{\omega }\left(x^{+}\right)$ after the expansion.

Figure 3

Schematics of quantum Hall edge current (red lines) (a) before and (b) after the expansion.