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

CC BY-SA 4.0
2022-04-18T08:31:25.563Z
What is the presentation of the complex vector that Alice has?
Vladimir Lysikov
CC BY-SA 4.0
2022-04-19T15:10:35.700Z
@VladimirLysikov Alice has each entry of the complex vector (up to some finite precision).
Yang
<quantum-computing><communication-complexity><quantum-information>
Quantum Communication Complexity Bound on Vector Inner Product
Yang
# Quantum Communication Complexity Bound on Vector Inner Product

(Asked by: username_0 on 2022-04-16)

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)?

**Tags:** quantum-computing, communication-complexity, quantum-information
> **Comments:**
> **username_1**: What is the presentation of the complex vector that Alice has?  
> **username_0**: @VladimirLysikov Alice has each entry of the complex vector (up to some finite precision).  

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