On teleportation

Question

I read about the teleportation in a simple explanation involving Alice and Bob. I understood the part where Alice and Bob are given one of the particle from an entangled pair. And then Alice measures state in Bell basis. And provides Bob with the operator to be operated.
I did understand that, but I am still curious to know what if Bob randomly picks the operator? And then Alice performs a measurement to know it. Will it affect the Alice's measurement? or would it be the same as Bob choosed?

Karl Pilkington · Accepted Answer

This is a good question. I believe it depends on the entangled state Alice and Bob share. The singlet state is rotationally invariant, so I guess for two-qubits which direction Bob picks to measure won't affect the protocol - if he is the first one measuring.
However, what is certain is that Alice cannot identify Bob's choice of measurement by measuring locally on her subsystem, since this would violate non-signalling. The only way to discover what Bob did is via classical communication.
"Will it affect the Alice's measurement?" - in a sense yes; this property of some entangled states is called steering - for a review https://arxiv.org/abs/1903.06663 . Bob can affect Alice's basis of local measurement, but if Bob and Alice do not share classical information, Alice won't know what Bob measured and the best she could do is guessing.

On teleportation

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