A hardware paper reports a depolarising channel in the form with .

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Quantum Information & Technology · Open quantum systems, decoherence and error correction

Quantum Information and Technology, Ch Noise as a quantum operation

Problem

A hardware paper reports a depolarising channel in the form (1−p′)ρ+p′3(XρX+YρY+ZρZ)(1-p')\rho + \frac{p'}{3}(X\rho X + Y\rho Y + Z\rho Z) with p′=0.15p' = 0.15. ((a)) Convert p′p' to the convention Dp(ρ)=(1−p)ρ+pI/2\mathcal{D}_p(\rho) = (1-p)\rho + pI/2, using p′=3p/4p' = 3p/4. ((b)) A qubit has Bloch vector r⃗=(0.6,0,0.8)\vec r = (0.6, 0, 0.8). Find its Bloch vector after Dp\mathcal{D}_p is applied.

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