Abstract
In this paper we analyze three quantum operations in two dimensional conformal field theories (CFTs): local projection measurements, creations of partial entanglement between two CFTs, and swapping of subsystems between two CFTs. We also give their holographic duals and study time evolutions of entanglement entropy. By combining these operations, we present an analogue of quantum teleportation between two CFTs and give its holographic realization. We introduce a new quantity to probe tripartite entanglement by using local projection measurement.
Highlights
P with the trace preserving condition i Ai A†i = j Bj Bj† = 1
Our quantum operations include local projection measurements and partial entangling of two conformal field theories (CFTs) as well as swapping of two CFTs
We would like to discuss the two different setups: (i) local projection measurement of a single CFT and (ii) partial entangling of two CFTs, at the same time as the computations are similar
Summary
We move onto to a gravity dual of (ii) partial entangling of two identical CFTs. As in the left picture, we glue two planes with two slits together.√ After the conformal transformation (2.9) into the annulus, we perform the map ζ = ρe 2w instead of (2.19). In the black hole phase τ2 > 1, the gravity dual of (i) local projection measurement is given by cutting a solid torus (= Euclidean BTZ geometry (4.7)) into a half as explained in the previous subsection. This space is sketched in figure 15.
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