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How to get the normalized post-measurement state?

Posted 6 days ago

I have this code to do a partial measurement on a 2-qubit system.

s=QuantumState["00"]/Sqrt[2]+QuantumState["01"]/Sqrt[6]+QuantumState["10"]I/Sqrt[6]+QuantumState["11"]/Sqrt[6];
s["Formula"]
(* measuring bit[1]*)
qmo=QuantumMeasurementOperator["ComputationalBasis",{1}];
qmo[s]["Probabilities"]
#["Formula"]&/@qmo[s]["StateAssociation"]

The issue is that the returned post-measurement states are not normalized. I'd appreciate it if anyone can let me know how to get the normalized states. Thank you!

Xiangyang Zhou

POSTED BY: Xiangyang Zhou
3 Replies

Use "Normalize": #["Normalize"]["Formula"]&/@qmo[s]["StateAssociation"]

POSTED BY: Nikolay Murzin

That solved my problem, thank you. Just curious, why doesn't "Formula" give the normalized form directly? Is there any use case for the unnormalized form?

POSTED BY: Xiangyang Zhou

"Formula" simply shows the amplitudes as they are stored. QuantumMeasurement "States" are not normalized by default (maybe we should add "NormalizedStates") because it easier to just project the underlying state without modifying any amplitudes, otherwise it can unnecessarily introduce some undesirable normalization factors in symbolic computation. It easier to normalize states if needed than simplifying more complex expressions.

POSTED BY: Nikolay Murzin
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