Private Quantum Database

TL;DR

The paper addresses the challenge of providing both user privacy and data privacy in database queries by encoding relational tuples as quantum states using Quantum Random Access Codes (QRACs) over Mutually Unbiased Bases (MUBs). It introduces a two-sided privacy framework (quantum SPIR) in which reading a chosen basis collapses the state and restricts access, controlled by a copy budget that trades retrieval fidelity against information leakage. The contributions include a concrete protocol for private queries, a blockwise QRAC encoding scheme with per-block budgets, and a hybrid quantum–classical architecture that is compatible with today’s Noisy Intermediate-Scale Quantum (NISQ) devices; preliminary simulations demonstrate feasible retrieval with bounded privacy leakage and scalability prospects. The work aims to shift the definition of quantum advantage from speedups to privacy guarantees, offering a practical pathway for privacy-preserving quantum databases in the near term. Key ideas include mapping keys to MUBs, encoding data blocks via QRACs, regenerating quantum states from classical descriptions at query time, and integrating quantum primitives into classical DBMS backends to support secure, hybrid deployments in the NISQ era.

Abstract

Quantum databases open an exciting new frontier in data management by offering privacy guarantees that classical systems cannot match. Traditional engines tackle user privacy, which hides the records being queried, or data privacy, which prevents a user from learning more than she has queried. We propose a quantum database that protects both by leveraging quantum mechanics: when the user measures her chosen basis, the superposition collapses and the unqueried rows become physically inaccessible. We encode relational tables as a sequence of Quantum Random Access Codes (QRACs) over mutually unbiased bases (MUBs), transmit a bounded number of quantum states, and let a single, destructive measurement reconstruct only the selected tuple. This allows us to preserve data privacy and user privacy at once without trusted hardware or heavyweight cryptography. Moreover, we envision a novel hybrid quantum-classical architecture ready for early deployment, which ensures compatibility with the limitations of today's Noisy Intermediate-Scale Quantum devices.

Figures (4)

• Figure 1: Example: Auditing with user and data privacy
• Figure 2: Bloch-sphere representation of $3\rightarrow 1$ QRAC, which encodes $3$ bits in a single qubit, and allows retrieval of any one of them with high probability. All possible single-qubit quantum states lie on the surface of the sphere
• Figure 3: Overview of our hybrid quantum-classical approach
• Figure 4: Quantum circuits for Alice to prepare any $2$-qubit state (dark grey) and for Bob to measure any $2$-qubit MUB (light grey). Each horizontal line represents a qubit that is transformed with quantum gates. The boxed $U_i$, $S$, $S^\dagger$ and $H$ are single-qubit gates typically implemented in photonics via waveplates, and the dot-line-circle symbol is a Controlled-NOT gate, typically implemented in photonics via interferometer setups.