EPR pairs, local projections and quantum teleportation in holography

Tokiro Numasawa, Noburo Shiba, Tadashi Takayanagi +1 more

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.

Tal Schwartzman, Antonio F. Rotundo, Raz Monsonego +1 more

Unlike standard quantum teleportation, many-body teleportation uses scrambling to transmit quantum information. In this protocol, initially localized information spreads over many degrees of freedom and is later refocused at the receiver by a simple coupling between the systems, followed by further many-body evolution. The protocol was developed from models of traversable wormholes in holography and has become a useful probe of scrambling. In particular, it can distinguish genuine scrambling from decoherence or noise when out-of-time-order correlators fail, and can reveal signatures of different scrambling mechanisms, including the distinctive behavior expected in holographic systems. Holography predicts that related protocols can transmit information between selected boundaries of multi-boundary wormhole geometries. Motivated by this setting, we study single-qubit many-body teleportation among three systems of qubits. The initial state consists of EPR pairs distributed among them, providing a simple analogue of an infinite-temperature three-boundary holographic state. We analyze the protocol with one-dimensional and all-to-all dynamics, both analytically and numerically using random circuits. We find that the third system suppresses teleportation once the spreading message reaches the region of qubits that are entangled with it. In one dimension, both the minimum coupling required for successful teleportation and the fidelity depend on the distance from the injection site to this region, a feature reminiscent of holographic causal shadows. For all-to-all dynamics, successful teleportation is instead restricted to early times and to sufficiently few qubits entangled with the third system. A third system therefore provides spatial, or subsystem, resolution of information spreading that is absent from the two-sided protocol. Our results offer a step toward many-body teleportation networks.

I. V. Sokolov, A. Gatti, Mikhail I. Kolobov +1 more

I. V. Sokolov, A. Gatti, Mikhail I. Kolobov +1 more

Arun Kumar Pati

Quantum teleportation requires 2 cbits to be sent from Alice to Bob in order to transmit an {\\em unknown} qubit provided they share an entangled EPR pair. Classical teleportation requires 2.19 cbits to be sent from Alice to Bob in order to transmit a {\\em known} qubit provided they share local hidden variables. We show that there is a simple scheme which requires 1 cbit to be sent from Alice to Bob for transmitting a {\\em known} qubit provided they share an entangled EPR pair. This suggests that the classical teleportation should be compared with the present scheme for comparing the cbit cost (1.19 cbits more) and the use of entanglement versus local hidden variables.

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