Introduction to Quantum Physics and Information Processing

202 Introduction to Quantum Physics and Information Processing

3

Z

2

Z Z

1

Z

|0i

H

•

H

x

|0i

H

•

H

y

FIGURE 10.8: Measuring Z

1

Z

2

and Z

2

Z

3

.

For a channel allowing a single qubit to change, we can estimate the min-

imum number of qubits needed to encode for error correction to work. We

already noted that the corrupted states |ψ

i

i are mutually orthogonal. Let’s vi-

sualize these states in the Hilbert space of three qubits, which is 8-dimensional.

Each of our corrupted states is a linear combination of two of the eight basis

vectors of H

8

, lying in a 2-d plane. Each of these planes would be mutually

orthogonal, since each of the component basis vectors is orthogonal to ...