Bound entangled states with a private key and their classical counterpart

TL;DR

This paper constructs bound-entangled quantum states with private keys from classical distributions, revealing a new classical analogue of bound entanglement and improving key rates, with implications for quantum and classical cryptography.

Contribution

It introduces a novel construction linking bound-entangled states with private keys to classical probability distributions, and proposes protocols to extract keys from these states.

Findings

States with higher key rates than previous work

Existence of a classical analogue of bound entanglement

Protocols extended to extract private keys from these states

Abstract

Entanglement is a fundamental resource for quantum information processing. In its pure form, it allows quantum teleportation and sharing classical secrets. Realistic quantum states are noisy and their usefulness is only partially understood. Bound-entangled states are central to this question---they have no distillable entanglement, yet sometimes still have a private classical key. We present a construction of bound-entangled states with private key based on classical probability distributions. From this emerge states possessing a new classical analogue of bound entanglement, distinct from the long-sought bound information. We also find states of smaller dimensions and higher key rates than previously known. Our construction has implications for classical cryptography: we show that existing protocols are insufficient for extracting private key from our distributions due to their "bound-entangled" nature. We propose a simple extension of existing protocols that can extract key from them.