EPR Pairs, Local Projections and Quantum Teleportation in Holography

TL;DR

This work develops a coherent framework for three quantum operations—local projection measurements, partial entangling, and partial swapping—within 2d CFTs and their holographic duals. By employing conformal maps, BCFT/AdS constructions, and holographic entanglement entropy, the authors reveal how these operations reshape entanglement structure over time and across coupled CFTs, including explicit results for free fermions and BTZ/AdS$_3$ geometries. A holographic analogue of quantum teleportation between CFTs is proposed, illustrating information transfer through Einstein-Rosen bridges and a temperature-adjusted BTZ setup. The paper also proposes a new tripartite entanglement probe, $\delta^B_A$, derived from local projections, to capture multipartite correlations beyond bipartite measures. These results illuminate how holography encodes complex quantum information processing and suggest avenues for higher-dimensional generalizations and refined multipartite entanglement diagnostics.

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.

Figures (24)

• Figure 1: The conformal transformation from the coordinate $(x,y)$ into an upper half plane $(\xi_1,\xi_2)$, where $w=(x+iy)/\sqrt{2}$ and $\xi=(\xi_1+i\xi_2)/\sqrt{2}$.
• Figure 2: The left picture describes the Euclidean path-integral expression of the quantum state, evolved by an Euclidean time after the projection measurement. The right picture describes the real-time evolution after the projection measurement.
• Figure 3: The conformal map between the two cut geometry and the cylinder
• Figure 4: The ratio $\frac{q}{p}$ as a function of $\rho$.
• Figure 5: The behavior of the growth of entanglement entropy $\Delta S_A$ in the free fermion CFT after the local projection measurement. The left graph describes $\Delta S_A$ as a function $x$, where the subsystem $A$ is chosen to be the interval $[-0.5+x,0.5+x]$. The right one shows the time evolution of $\Delta S_A$ for the fixed subsystem $A$ given by $[-0.5,0.5]$.