[Paper Review] Limitations on device independent secure key via squashed non-locality

Marek Winczewski, Tamoghna Das+1 more|arXiv (Cornell University)|Mar 28, 2019

Quantum Information and Cryptography4 citations

TL;DR

This paper establishes upper bounds on device-independent quantum key distribution (DIQKD) security against non-signaling adversaries using a novel technique called 'squashing' applied to secrecy monotones. It introduces 'squashed non-locality' as a computable, convex, and asymptotically continuous upper bound on non-signaling device-independent (NSDI) key rates, proving that PR-box mixtures with PR weight below 80% cannot distill key via MDLOPC operations, thus showing non-locality does not guarantee secrecy.

ABSTRACT

We initiate a systematic study to provide upper bounds on device-independent key, secure against a non-signaling adversary (NSDI), distilled by a wide class of operations, currently used in both quantum and non-signaling device-independent protocols. These operations consist of a direct measurements on the devices followed by Local Operations and Public Communication (MDLOPC). We employ the idea of squashing on the secrecy monotones, which provide upper bounds on the key rate in secret key agreement (SKA) scenario, and show that secrecy monotones are the upper bounds on NSDI key. As an important instance, an upper bound on NSDI key rate called squashed non-locality, has been constructed. It exhibits several important properties, including convexity, monotonicity, additivity on tensor products, and asymptotic continuity. Using this bound, we identify numerically a domain of two binary inputs and two binary outputs non-local devices for which the non-locality is zero, and therefore one can not distil key from them via MDLOPC operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with the weight of PR box less than $80\%$. This example confirms the intuition that non-locality need not imply secrecy in the non-signaling scenario. The approach is general, describing how to construct other tighter yet possibly less computable upper bounds. Our technique for obtaining upper bounds is based on the non-signaling analog of quantum purification: the complete extension, which yields equivalent security conditions as previously known in the literature.

Motivation & Objective

• To establish rigorous upper bounds on device-independent key distillation under non-signaling attacks.
• To analyze the limitations of MDLOPC operations in distilling secure keys from non-local correlations.
• To formalize a non-signaling analog of quantum purification via complete extension for security analysis.
• To identify conditions under which non-locality fails to yield secure key, even when non-locality is present.
• To develop a general framework for constructing tighter, computable upper bounds on NSDI key rates.

Proposed method

• Applies the concept of 'squashing' to secrecy monotones to derive upper bounds on non-signaling device-independent key rates.
• Introduces 'squashed non-locality' as a new measure that inherits convexity, monotonicity, and asymptotic continuity.
• Uses the non-signaling analog of quantum purification—'complete extension'—to derive equivalent security conditions.
• Employs MDLOPC operations (measurements followed by local operations and public communication) as the class of allowed protocols.
• Analyzes the structure of two-input, two-output non-local boxes, particularly mixtures of PR and anti-PR boxes.
• Numerically evaluates the domain where non-locality vanishes, indicating no key can be distilled.

Experimental results

Research questions

• RQ1 Can non-locality alone guarantee secure key distillation in the non-signaling scenario?
• RQ2 What are the fundamental limitations of MDLOPC operations in distilling device-independent keys?
• RQ3 How can secrecy monotones be adapted to provide upper bounds on non-signaling device-independent key rates?
• RQ4 What is the role of non-locality in determining the maximum achievable key rate under non-signaling attacks?
• RQ5 Can a general framework be constructed to derive tighter upper bounds on NSDI key rates?

Key findings

• Squashed non-locality is a valid upper bound on non-signaling device-independent key rates, exhibiting convexity and asymptotic continuity.
• The measure is additive under tensor products, enabling analysis of multiple non-local boxes.
• For two-binary-input, two-binary-output non-local boxes, non-locality vanishes when the PR-box weight is below 80%.
• Mixture of PR and anti-PR boxes with PR weight less than 80% cannot distill any secure key via MDLOPC operations.
• Non-locality does not imply secrecy in the non-signaling scenario, confirming that non-locality is neither necessary nor sufficient for key distillation.
• The method provides a general framework to construct tighter upper bounds, even if computationally more demanding.