Quantum Key Recycling with 8-state encoding (The Quantum One-Time Pad is more interesting than we thought)

B. Skoric, M. de Vries

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
125 Downloads (Pure)


Perfect encryption of quantum states using the Quantum One-Time Pad (QOTP) requires two classical key bits per qubit. Almost-perfect encryption, with information-theoretic security, requires only slightly more than 1. We slightly improve lower bounds on the key length. We show that key length n+2log1ε
suffices to encrypt n
qubits in such a way that the cipherstate’s L 1
-distance from uniformity is upperbounded by ε
. For a stricter security definition involving the ∞

-norm, we prove sufficient key length n+logn+2log1ε +1+1n log1δ +logln21−ε
, where δ
is a small probability of failure. Our proof uses Pauli operators, whereas previous results on the ∞

-norm needed Haar measure sampling. We show how to QOTP-encrypt classical plaintext in a nontrivial way: we encode a plaintext bit as the vector ±(1,1,1)∕3 – √
on the Bloch sphere. Applying the Pauli encryption operators results in eight possible cipherstates which are equally spread out on the Bloch sphere. This encoding, especially when combined with the half-keylength option of QOTP, has advantages over 4-state and 6-state encoding in applications such as Quantum Key Recycling (QKR) and Unclonable Encryption (UE). We propose a key recycling scheme that is more efficient and can tolerate more noise than a recent scheme by Fehr and Salvail. For 8-state QOTP encryption with pseudorandom keys, we do a statistical analysis of the cipherstate eigenvalues. We present numerics up to nine qubits.
Original languageEnglish
Article number1750016
Number of pages32
JournalInternational Journal of Quantum Information
Issue number3
Publication statusPublished - Apr 2017


  • Key recycling
  • Quantum cryptography
  • Quantum one-time pad

Cite this