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Say Alice has a (complex) vector $a\in\mathbb{C}^d$, and interacts with Bob in a quantum communication protocol (sending qubits back and forth). At the end of the protocol, Bob produces a guess $b\in\mathbb{C}^d$ for Alice's vector. Do we know of upper bounds on $\langle a|b\rangle$ in terms of the quantum communication complexity (e.g. number of qubits communicated)?

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  • $\begingroup$ What is the presentation of the complex vector that Alice has? $\endgroup$ Apr 18, 2022 at 8:31
  • $\begingroup$ @VladimirLysikov Alice has each entry of the complex vector (up to some finite precision). $\endgroup$
    – Yang
    Apr 19, 2022 at 15:10

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