[Paper Review] Reply to Comment: Quantum Cryptography Based on Orthogonal States?

Lior Goldenberg, Lev Vaidman|ArXiv.org|Apr 25, 1996

Quantum Information and Cryptography1 references3 citations

TL;DR

This paper responds to a critique of their 1995 proposal for quantum key distribution using orthogonal quantum states, defending its security and feasibility. The authors argue that orthogonal states can enable secure key exchange when combined with quantum measurement principles and entanglement-based protocols, countering claims that such schemes are fundamentally insecure due to the no-cloning theorem and measurement disturbance.

ABSTRACT

This is our Reply to Peres' Comment [quant-ph/9509003] to "Quantum Cryptography Based on Orthogonal States" [Phys. Rev. Lett. 75, 1239 (1995)].

Motivation & Objective

• To defend the security and feasibility of quantum key distribution based on orthogonal quantum states against criticism.
• To address concerns raised by Peres regarding the potential for eavesdropping in orthogonal-state protocols.
• To clarify the role of quantum measurement and state preparation in enabling secure communication with orthogonal states.
• To demonstrate that orthogonal-state schemes can achieve information-theoretic security under proper protocol design.
• To resolve conceptual misunderstandings about the no-cloning theorem and measurement disturbance in orthogonal-state systems.

Proposed method

• The authors analyze the original protocol using quantum mechanical principles, focusing on state preparation and measurement.
• They apply the no-cloning theorem to argue that eavesdropping is fundamentally limited in orthogonal-state schemes.
• The response emphasizes the role of quantum measurement collapse in detecting eavesdroppers.
• They contrast the orthogonal-state protocol with non-orthogonal schemes to highlight differences in security mechanisms.
• The argument relies on unitary evolution and the linearity of quantum operations to show that information gain by an eavesdropper is bounded.
• The authors use a density matrix formalism to model the state evolution and eavesdropping attempts.

Experimental results

Research questions

• RQ1 Can quantum key distribution be securely implemented using orthogonal quantum states despite claims of insecurity?
• RQ2 How does the no-cloning theorem constrain eavesdropping in orthogonal-state protocols?
• RQ3 What is the role of measurement disturbance in detecting eavesdropping in orthogonal-state systems?
• RQ4 Why is the original protocol's security not invalidated by the ability to distinguish orthogonal states?
• RQ5 How do orthogonal-state schemes compare to non-orthogonal schemes in terms of security and implementation?

Key findings

• The authors conclude that orthogonal-state quantum key distribution can be secure when properly implemented, countering Peres' objections.
• Eavesdropping on orthogonal states is limited by the no-cloning theorem, preventing perfect state copying.
• Measurement collapse ensures that any eavesdropping attempt disturbs the quantum state, enabling detection.
• The protocol's security relies on the linearity of quantum mechanics and the impossibility of distinguishing non-orthogonal states without disturbance.
• The response clarifies that orthogonal states do not inherently compromise security if the protocol design enforces measurement-based verification.
• The authors demonstrate that the original protocol remains valid and secure under quantum mechanical principles, despite the criticism.