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Clarification on "Bob must do the same thing to every pair of electrons" in Quantum Computing for Everyone (Superdense Coding)

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⚡ Quantum Brief
A 2025 Stack Exchange discussion clarifies a key superdense coding concept from Quantum Computing for Everyone, focusing on Bob’s role in decoding Alice’s two-bit message using entangled electron pairs. Bob must apply a fixed quantum circuit—CNOT followed by Hadamard—to every received pair, regardless of Alice’s intended message, because he lacks prior knowledge of her input. The uniformity ensures Bob’s measurements yield the correct classical bits (00, 01, 10, or 11) without additional communication, preserving the protocol’s no-signaling principle. The confusion arose from the text’s emphasis on Bob’s passive role: his actions are predetermined and identical for all cases, distinguishing superdense coding from classical methods. This highlights how quantum protocols rely on fixed local operations to extract information from entanglement, a foundational insight for quantum communication systems.
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Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Stack Overflow for Teams is now called Stack Internal. Bring the best of human thought and AI automation together at your work. Bring the best of human thought and AI automation together at your work. Learn more Stack InternalKnowledge at workBring the best of human thought and AI automation together at your work.I am reading $\textit{Quantum Computing for Everyone}$ by Chris Bernhardt and I came across the following passage in the section on $\textbf{Superdense coding}$:Alice and Bob initially have one electron each. Eventually, Bob is going to have both electrons and is going to measure their spins. Bob will have some quantum circuit with two wires exiting. If Alice wants to send 00, we need to arrange things so that just before Bob starts measuring, the top electron is in state $\lvert 0 \rangle$ and the bottom electron is in state $\lvert 0 \rangle$, that is, the pair of electrons is in the unentangled state $\lvert 00 \rangle$ just before Bob measures their spins. Similarly, if Alice wants to send 01, we want the pair of electrons to be in the state $\lvert 01 \rangle$ just before Bob makes his measurements. The final state should be $ > |10 \rangle$ if Alice wants to send 10, and $\lvert 11 \rangle$ if Alice wants to send 11.I follow this part, but the next paragraph confuses me:The final observation is that Bob must do the same thing to every pair of electrons that he receives. He cannot do different things depending on what Alice is trying to send, because he doesn’t know what she is trying to send. That’s the whole point!Could anyone please elaborate on what it means that "Bob must do the $\textbf{same thing}$ to every pair of electrons that he receives. He cannot do $\textbf{different things}$"?It probably means that Bob has to perform the same circuit for each pair - namely, CNOT controlled by the qubit sent by Alice onto the qubit held by Bob, then Hadamard on the qubit held by Bob, and measure both elements of the pair in the computational basis. It's probably just meant to emphasize that all of Bob's actions are local to him, with no further communication from Alice.Thanks for contributing an answer to Quantum Computing Stack Exchange!But avoid …Use MathJax to format equations. MathJax reference.To learn more, see our tips on writing great answers.Required, but never shown By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answersFind the answer to your question by asking.Explore related questionsSee similar questions with these tags.To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Site design / logo © 2025 Stack Exchange Inc; user contributions licensed under CC BY-SA . rev 2025.11.24.37235

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