Scrambling and Quantum Teleportation

TL;DR

This paper explores the relationship between quantum scrambling and teleportation fidelity, proposing a conjecture that maximal scrambling enhances teleportation accuracy, supported by analytical and numerical evidence.

Contribution

It introduces a 7-qubit quantum circuit for teleportation and conjectures a proportional relationship between scrambling and fidelity, tested with analytical and numerical methods.

Findings

Maximal scrambling unitary enables perfect teleportation.

Fidelity depends on the choice of qubits for Bell measurement.

Conjecture about scrambling and fidelity is conditionally supported.

Abstract

Scrambling is a concept introduced from information loss problem arising in black hole. In this paper we discuss the effect of scrambling from a perspective of pure quantum information theory. We introduce $7$-qubit quantum circuit for a quantum teleportation. It is shown that the teleportation can be perfect if a maximal scrambling unitary is used. From this fact we conjecture that ``the quantity of scrambling is proportional to the fidelity of teleportation''. In order to confirm the conjecture we introduce $\theta$-dependent partially scrambling unitary, which reduces to no scrambling and maximal scrambling at $\theta = 0$ and $\theta = \pi / 2$, respectively. Then, we compute the average fidelity analytically, and numerically by making use of qiskit (version $0.36.2$) and $7$-qibit real quantum computer ibm$\_$oslo. Finally, we conclude that our conjecture can be true or false depending on the choice of qubits for Bell measurement.