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

B. Skoric, M. de Vries

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Abstract


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
n+2log1ε
suffices to encrypt n
n
qubits in such a way that the cipherstate’s L 1
L1
-distance from uniformity is upperbounded by ε
ε
. For a stricter security definition involving the ∞

-norm, we prove sufficient key length n+logn+2log1ε +1+1n log1δ +logln21−ε
n+logn+2log1ε+1+1nlog1δ+logln21−ε
, where δ
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 – √
±(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
Volume15
Issue number3
DOIs
Publication statusPublished - Apr 2017

Keywords

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

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