Abstract
In this paper, we propose a concrete teleportation protocol in the SYK model based on a particle traversing a wormhole. The required operations for the communication, and insertion and extraction of the qubit, are all simple operators in terms of the basic qubits. We determine the effectiveness of this protocol, and find a version achieves almost perfect fidelity. Many features of semiclassical traversable wormholes are manifested in this setup.
Highlights
Found in [1] is that the gravitational backreaction to quantum effects induced by generic couplings between the exterior regions of the pair of black holes can render the wormhole traversable
In this paper, we propose a concrete teleportation protocol in the SYK model based on a particle traversing a wormhole
We propose a precise teleportation protocol using N qubit fermionic systems that correspond to gravity in a nearly AdS2 black hole spacetime
Summary
Consider 5 systems: R, Q, l, r, T. The second step can equivalently be replaced by measurement on the left together with action of a unitarity operator on the right, so that only a classical channel communication is required. From (2.24) and (2.25), we can derive χrU χ†l χl |tfd = χrU |tfd , χ†rU χlχ†l |tfd = χ†rU |tfd (2.26) (2.27) This has a clear physical interpretation: the left-right causal propagator reaches its maximum value. For the second possible case above, the condition for perfect teleportation is similar ρ11 = 0 =⇒ χ†rU χlχ†l |tfd = χ†rU χl |tfd = 0 ρ44 = 0 =⇒ χrU χ†l |tfd = χrU χ†l χl |tfd = 0 |ρ23| = 1 =⇒ {U †χrU , χl} = 1. If we interpret χ† as creation of a particle and χ as annihilation of a particle, it is natural to take the first case
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