Security of two-way quantum key distribution

Abstract

Quantum key distribution protocols typically make use of a one-way quantum channel to distribute a shared secret string to two distant users. However, protocols exploiting a two-way quantum channel have been proposed as an alternative route to the same goal, with the potential advantage of outperforming one-way protocols. Here we provide a strategy to prove security for two-way quantum key distribution protocols against the most general quantum attack possible by an eavesdropper. We utilize an entropic uncertainty relation, and only a few assumptions need to be made about the devices used in the protocol. We also show that a two-way protocol can outperform comparable one-way protocols

Finite Key Size Analysis of Two-Way Quantum Cryptography

“…It is however more resource demanding as it requires the use of a quantum memory on Bob's side. Our description of SDC here follows closely that of [5]. Very simply, the SDC protocol sees Bob sending half a Bell pair to Alice (while storing the other half in a quantum memory) for her to encode by virtue of a randomly chosen unitary transformation from the set containing the identity operator and the three Pauli operators, {I, σ x , σ y , σ z }.…”

“…In the original LM05 protocol, apart from p X = p Z , only two unitary transformations were considered, namely the passive I and iσ y . In [5], a generalization was made to include another two unitary transformation, namely the σ x and σ z , and the possibility of having different probabilities p X and p Z . In this protocol, upon executing her unitary transformation, Alice would resubmit the qubit to Bob who would measure in the same basis he prepared in.…”

“…However, despite its early introduction in 2002 [3], and varying versions that followed, it was only about a decade later that a proper proof for one specific two-way protocol was found for unconditional security in [4] and a proof for a purified version was reported in [5]. In [4], the proof was done for the specific case of non-entangled qubits in one of four states coming from two mutually unbiased bases (this protocol has been referred to as LM05 [6] and we shall refer to it as such hereafter).…”

“…The central feature of this work is a review of the security analysis done based on protocol purifications in [5] and a natural generalization to the the case for finite sized keys. We begin with a quick description of two most relevant two-way QKD protocols followed by their purifications.…”

“…In [4], the proof was done for the specific case of non-entangled qubits in one of four states coming from two mutually unbiased bases (this protocol has been referred to as LM05 [6] and we shall refer to it as such hereafter). In [5], a purification of two two-way QKD protocol, namely the Super Dense Coding scheme (SDC) and LM05 was done in order to provide a security proof.…”