Scrambling and quantum teleportation

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 regardless of the information loss problem. 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 $$\theta $$ θ -dependent partially scrambling unitary, which reduces to no scrambling and maximal scrambling at $$\theta = 0$$ θ = 0 and $$\theta = \pi / 2$$ θ = π / 2 , respectively. Then, we compute the average fidelity analytically, and numerically by making use of qiskit (version 0.36.2) and 7-qubit real quantum computer ibm $$\_$$ _ oslo. Finally, we show that our conjecture can be true or false depending on the choice of qubits for Bell measurement.