Bound entangled states with secret key and their classical counterpart

Entanglement is a fundamental resource for quantum information processing. In its pure form, it allows quantum teleportation [1] and sharing classical secrets [2]. 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 [3], yet sometimes still have a private classical key [4, 5]. We present a new and unexpected construction of bound entangled states with private key based on classical probability distributions. This construction gives a remarkable and long-sought classical analogue of bound entanglement [6–9]. 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.