Physical Underpinnings of Privacy

Abstract

One of the remarkable features of quantum mechanics is the ability to ensure secrecy. Private states embody this effect, as they are precisely those multipartite quantum states from which two parties can produce a shared secret that cannot in any circumstance be correlated to an external system. Naturally, these play an important role in quantum key distribution (QKD) and quantum information theory. However, a general distillation method has heretofore been missing. Inspired by Koashi's complementary control scenario (arXiv:0704.3661v1 [quant-ph]), we give a new definition of private states in terms of one party's potential knowledge of two complementary measurements made on the other and use this to construct a general method of private state distillation using quantum error-correcting codes. The procedure achieves the same key rate as recent, more information-theoretic approaches while demonstrating the physical principles underlying privacy of the key. Additionally, the same approach can be used to establish the hashing inequality for entanglement distillation, as well as the direct quantum coding theorem.

12.5 pages

References in corpus (26)

• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Good Quantum Error-Correcting Codes Exist
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Encoding a qubit in an oscillator
• Security of quantum key distribution using d-level systems
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Multiple Particle Interference and Quantum Error Correction
• Distillation of secret key and entanglement from quantum states
• The capacity of the noisy quantum channel
• An information-theoretic security proof for QKD protocols
• Secure key from bound entanglement
• Fast and simple one-way Quantum Key Distribution
• Lower and upper bounds on the secret key rate for QKD protocols using one--way classical communication
• Locking classical correlation in quantum states
• A decoupling approach to the quantum capacity
• Unconditionally Secure Key Distribution Based on Two Nonorthogonal States
• Relating quantum privacy and quantum coherence: an operational approach
• Classical data compression with quantum side information
• Quantum privacy and quantum coherence
• Unconditional Security of Three State Quantum Key Distribution Protocols
• Unconditionally secure key distillation from multi-photons
• Quantum key distribution based on private states: unconditional security over untrusted channels with zero quantum capacity
• Generalized decoding, effective channels, and simplified security proofs in quantum key distribution
• Noisy Preprocessing and the Distillation of Private States
• Method for decoupling error correction from privacy amplification
• Random quantum codes from Gaussian ensembles and an uncertainty relation

Cited by in corpus (31)

• Quantum entanglement
• Entropic Uncertainty Relations and their Applications
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• Conjectured Strong Complementary Information Tradeoff
• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Quantum-memory-assisted entropic uncertainty relations
• The information-theoretic costs of simulating quantum measurements
• One-Shot Classical Data Compression with Quantum Side Information and the Distillation of Common Randomness or Secret Keys
• Efficient Quantum Polar Coding
• Polar codes for private and quantum communication over arbitrary channels
• Multipartite secret key distillation and bound entanglement
• Duality of privacy amplification against quantum adversaries and data compression with quantum side information
• Sequential decoding of a general classical-quantum channel
• Quantum polar codes for arbitrary channels
• Polar codes for degradable quantum channels
• Improved quantum entropic uncertainty relations
• Leftover hashing from quantum error correction: Unifying the two approaches to the security proof of quantum key distribution
• Efficient Quantum Polar Codes Requiring No Preshared Entanglement
• A transform of complementary aspects with applications to entropic uncertainty relations
• Duality of channels and codes
• The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
• Polar codes for private classical communication
• Bounds on Information Combining With Quantum Side Information
• Optimal State Merging Without Decoupling
• W-like bound entangled states and secure key distillation
• Optimal Universal Uncertainty Relations
• Performance of polar codes for quantum and private classical communication
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• The reduction of entropy uncertainty for qutrit system under non-Markov noisy environment
• The dynamics of entropy uncertainty for qutrit system under the random telegraph noise
• Equivalence of three classical algorithms with quantum side information: Privacy amplification, error correction, and data compression