Performing Bell State Measurement in Teleportation

[ljagerman]

Most protocols on Quantum Teleportation (using Alice and Bob as performers) include a crucial step where Alice performs a Bell State Measurement. Usually the applicable math is given in the protocol, but many protocols make the following kind of statement with no explanation: "Alice must rotate her measurement apparatus to align with the Bell basis."

If you can, please clarify
(1) what devices or parts of the apparatus need to be rotated (?? beam splitters, gates, crystals) and where are these devices installed,
(2) how does Alice know by how much to rotate these,
(3) what are the mathematical effects of this action (e.g. how is the superposition changed), and
(4) what is the relationship between this action and the unitary operations Bob must perform to recover the teleported state?

Thank You!
Lou Jagerman

 

[Strilanc]

Could you link to something actually saying "rotate to align with the Bell basis"? That's a really strange statement, given the nature of the Bell basis.

Anyways, here's a relevant paper and here's a relevant wikipedia article.

 

[ljagerman]

Hello,
The source is

http://quantumfrontiers.com/2012/09/17/how-to-build-a-teleportation-machine-teleportation-protocol/

The pertinent quote in the text is "..., Alice rotated her apparatus to align with the Bell basis, and by doing so, the entangled state of her qubits was transformed to what's written above. The pages are not numbered but the paragraph with this quote begins with "This equation may seem beastly..."

As I said in my question, the quantum math (showing the states and such) in this process is (sort of) explained. However, the physical rotation of some device in the experiment is not described at all.

Thanks you your interest! Any help will be appreciated!

Lou

 

[Strilanc]

Because the Bell basis involves two qubits, and rotations are usually associated with the state of a single qubit (i.e. the Bloch sphere), I have no idea what physical movement they have in mind when they say "rotate the apparatus to align with the Bell basis". Maybe they just use the word 'rotate' as a stand-in for 'any unitary basis change achieved by equipment'. When I imagine a bell basis measurement I imagine beam splitters and detectors arranged in ways described by the wikipedia article I linked to, or just the raw CNOT+H of quantum logic circuits.

The post you linked to seems overall pretty good to me. I've written similar content in the past. It doesn't really cover much more, but the phrasing will be different: Storing Bandwidth with Quantum Teleportation and Quantum Teleportation's Two Functions. Also you can play with a quantum teleportation circuit in Quirk.

 

[ljagerman]

Thanks! I can go on from here. Much appreciated,
Lou