Communication-Optimal Blind Quantum Protocols

TL;DR

This work establishes a tight, entropy-based lower bound on the quantum communication required for information-theoretically secure blind quantum computation under Pauli padding, showing the minimal cost is $E(N) \ge 2n - r$ with $r = \dim(\mathcal{P}_{\mathcal{F}})$. It develops Pauli padding and the preserved Pauli subspace framework to decompose target gates and track padding through circuits, then constructs a saturating protocol that achieves the bound, including a Clifford-special case where separable states suffice. The RM and PS variants are analyzed, with an explicit entropy accounting and a demonstration of optimality via a standard Clifford-based transformation. The results illuminate how to minimize quantum communication while preserving blindness and identify open directions for padding beyond Pauli structures and broader gate sets.

Abstract

A user, Alice, wants to get server Bob to implement a quantum computation for her. However, she wants to leave him blind to what she's doing. What are the minimal communication resources Alice must use in order to achieve information-theoretic security? In this paper, we consider a single step of the protocol, where Alice conveys to Bob whether or not he should implement a specific gate. We use an entropy-bounding technique to quantify the minimum number of qubits that Alice must send so that Bob cannot learn anything about the gate being implemented. We provide a protocol that saturates this bound. In this optimal protocol, the states that Alice sends may be entangled. For Clifford gates, we prove that it is sufficient for Alice to send separable states.

Figures (3)

• Figure 1: General circuit used for RM optimal blind quantum computing. Bob entangles his state $\ket{\psi}$ with an additional $\text{dim}(\mathcal{B})=2n-r$ qubits which are then sent to Alice.
• Figure 2: General Receive & Measure protocol. Bob starts with his state $\rho$ and additional ancilla states. In each round, Alice sends Bob a message. Bob responds with a classical message and some quantum communication, which Alice measures. By the end, Bob holds an encrypted version of his state with $U^d$ enacted, and Alice knows the encryption key.
• Figure 3: General circuit used for optimal blind quantum computing where Alice is capable of PS. Alice prepares the state $\ket{\phi_U}$, which is sent to Bob. The state is input into the circuit with Bob's state $\ket{\psi}$.

Theorems & Definitions (22)

• Lemma 1
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof
• Lemma 5
• proof
• Theorem 1: Resource bound