Measurement and Decoherence

The measurement issues spill over into another aspect of quantum states—an aspect that is of major concern for QC. This problem is called decoherence. We design our measurement devices to interact with our qubits at specified times and locations. However, the qubits are not completely isolated from their surroundings—their environments. Most often, the environment has electromagnetic fields (thermal radiation, light, electric fields) and molecular interactions, for example, that affect our qubits. Those interactions mean that we need to take the quantum states of the environment into account when describing the behavior of our qubits. In essence, the overall system (qubits plus the environment, which is, of course, nothing more than a vast collection of qubits itself) is described by an entangled state. We distinguish this situation from a measurement interaction because often (almost always) we have no control over the interaction of our qubits with the environment. As we discussed in the previous section, we build a measurement device so that only certain of its states are correlated with our qubit’s states.

To take the environment into account, we could write the state of qubit plus environment as

$$\underbrace{|A_0\rangle}_\text{qubit state} \underbrace{\{c_a | e_a\rangle + c_b |e_b\rangle + \cdots\},}_\text{state of the environment}$$