The Quantum One-Time Pad and Private-Key Encryption of Qubits
Stub. Encrypting quantum states and the security games (adversary-vs-challenger, multi-message security) used to define it; LWE-based classical encryption and decryption, and how to tolerate the noise LWE introduces; the Pauli X and Z gates and their action on the Bloch sphere as the quantum analogue of a classical one-time pad's XOR; and the resulting quantum one-time pad (QOTP) and full definition of private-key encryption of qubits, with correctness and security.
Corresponds to Chapters 16–17. Encrypting a quantum state needs its own security game formalism (an adversary-vs-challenger game, extended to multi-message security) since the “ciphertext” is itself a quantum state subject to no-cloning and measurement disturbance. Works through LWE-based encryption/decryption concretely, including how to handle the inherent noise LWE’s hardness relies on without it corrupting correctness. The Pauli X and Z gates (bit-flip and phase-flip, acting as point reflections of the Bloch sphere — see unitary-dynamics-and-quantum-circuits for the general /Bloch- sphere picture these specialize) are exactly the right building block: applying a uniformly random and to a qubit (the quantum one-time pad, QOTP) perfectly randomizes it regardless of its original state, the direct quantum generalization of XOR-ing with a random classical bit. Closes with the full definition of private-key encryption of qubits and its correctness/security proofs.
Outline (TODO — flesh out each)
- Encrypting quantum states — the adversary-vs-challenger game
- Multi-message security
- LWE encryption and decryption; resolving the presence of errors
- The Pauli X gate; the Pauli Z gate; action on the Bloch sphere
- The quantum one-time pad (QOTP)
- Private-key encryption of qubits — correctness and security