Bound entangled states with a private key and their classical counterpart

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.

This version matches with the published version and includes changes suggested by referees. We added a new appendix on distillation with remanent devices and also discuss the 4x5 example in more detail. A Mathematica notebook with source code is included

References in corpus (4)

• Quantum Communication With Zero-Capacity Channels
• Experimental multiparticle entanglement dynamics induced by decoherence
• Experimental bound entanglement in a four-photon state
• Experimental Extraction of Secure Correlations from a Noisy Private State

Cited by in corpus (18)

• Quantum mechanical which-way experiment with an internal degree of freedom
• Round Complexity in the Local Transformations of Quantum and Classical States
• The platypus of the quantum channel zoo
• Bounds on quantum nonlocality via partial transposition
• Bounding quantum capacities via partial orders and complementarity
• Family of Bell inequalities violated by higher-dimensional bound entangled states
• A class of genuinely high-dimensionally entangled states with a positive partial transpose
• Distributions Attaining Secret Key at a Rate of the Conditional Mutual Information
• A Classical Analog to Entanglement Reversibility
• Broadcasting of quantum correlations in qubit-qudit systems
• Increasing distillable key rate from bound entangled states by using local filtration
• Bipartite Bound Entanglement
• Constraints on Multipartite Quantum Entropies
• Random private quantum states
• Robust entanglement measure for mixed quantum states
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Quantum Versus Classical Advantages in Secret Key Distillation (and Their Links to Quantum Entanglement)
• Construction and properties of a class of private states in arbitrary dimensions