 Quote by A. Neumaier
in quantum computing they clearly distinguish between measurements and quantum circuits of the kind we discussed, so there must have been a misunderstanding since you wrote:
Quote by Hurkyl
I am under the impression that it's rather standard to allow "measurement" to apply to the indefinite case as well.
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Since you apparently quit the discussion just at the point where the crucial gap in your argument had been identified, let me summarize the findings of our extended discussion:
Our CNOT gate discussion started with your claim that it is a measurement device:
Quote by Hurkyl
Let's start with something possibly very simple. I consider a CNOT gate ( wikipedia link) a measuring device. It measures the qubit on its control line, and records the result of measurement by adding it to the target line. |
Our discussion revealed that
if each target line is initialized with a definite zero state, CNOT gates can be used to construct an ancilla for a sequence of quasi-measurements, such that the reduced density matrix on the output control line is decohered, i.e., diagonal. Therefore different observers see the same result, conditioned on a particular measurement result for one observer.
But this doesn't hold for CNOT gates that are differently prepared. This shows that the CNOT gate by itself is not a measurement device, but only the dissipative system that consists of
the CNOT gate together with another gate that prepares the target line in a definite zero state. The latter requires already a definite outcome of a measurement, and hence must be itself a measurement device.
Indeed, in quantum information theory, one has specific measurement gates that perform a binary projective measurement and produce a definite outcome. These gates exist as real devices, and are necessary for any quantum information technology.
Thus while CNOT gates explain the working of decoherence in a very elegant and simple way, they - like decoherence itself - do not explain the working of measurement gates (or any other measurement devices).