Security bound of two-bases quantum key-distribution protocols using qudits

Abstract

We investigate the security bounds of quantum cryptographic protocols using $d$-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the BB84 quantum key distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.

12 pages, 2 figures, to appear in Phys. Rev. A

References in corpus (40)

• Quantum Cryptography
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Quantum Key Distribution with High Loss: Toward Global Secure Communication
• Security of quantum key distribution using d-level systems
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Optimal eavesdropping in quantum cryptography with six states
• Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations
• Quantum Cryptography with Coherent States
• A new proof for the existence of mutually unbiased bases
• Quantum cryptography with 3-state systems
• Quantum Key Distribution over 67 km with a plug & play system
• Practical free-space quantum key distribution over 10 km in daylight and at night
• Quantum Cryptography using larger alphabets
• Optimal eavesdropping in cryptography with three-dimensional quantum states
• Secure key from bound entanglement
• Entanglement as precondition for secure quantum key distribution
• Secure quantum key distribution using squeezed states
• Security of Quantum Key Distribution with Entangled Qutrits
• Unconditionally Secure Key Distribution Based on Two Nonorthogonal States
• Unconditional security of coherent-state quantum key distribution with strong phase-reference pulse
• Security of Quantum Key Distribution with entangled quNits
• Tailoring photonic entanglement in high-dimensional Hilbert spaces
• Quantum key distribution for d-level systems with generalized Bell states
• Separability and distillability in composite quantum systems -a primer-
• Coherent eavesdropping strategies for the 4-state quantum cryptography protocol
• Efficient bipartite quantum state purification in arbitrary dimensional Hilbert spaces
• Unconditional Security of the Bennett 1992 quantum key-distribution over lossy and noisy channel
• Unconditionally Secure Key Distribution In Higher Dimensions By Depolarization
• Quantum Key Distribution using Multilevel Encoding: Security Analysis
• Quantum key distribution over 30km of standard fiber using energy-time entangled photon pairs: a comparison of two chromatic dispersion reduction methods
• Quantum correlations and secret bits
• Detecting two-party quantum correlations in quantum key distribution protocols
• Equivalence between two-qubit entanglement and secure key distribution
• Practical Realization of the Quantum Cryptography Protocol Exploiting Polarization Encoding in the Qutrits

Cited by in corpus (29)

• Quantum entanglement
• Advances in Quantum Cryptography
• Security Proof for Quantum Key Distribution Using Qudit Systems
• Overcoming Noise in Entanglement Distribution
• Protecting qutrit-qutrit entanglement by weak measurement and reversal
• Quantum Cloning Machines and the Applications
• Quantum key distribution overcoming extreme noise: simultaneous subspace coding using high-dimensional entanglement
• Security of high-dimensional quantum key distribution protocols using Franson interferometers
• Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication
• Quantum key distribution with quantum walks
• Securing quantum key distribution systems using fewer states
• Symmetries and security of a quantum-public-key encryption based on single-qubit rotations
• Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions
• Information communicated by entangled photon pairs
• Reference-frame-independent design of phase-matching quantum key distribution
• General Quantum Key Distribution in Higher Dimension
• Distribution of quantum Fisher information in asymmetric cloning machines
• Equi-entangled bases in arbitrary dimensions
• Symmetries of the finite Heisenberg group for composite systems
• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• Probing Quantum Telecloning on Superconducting Quantum Processors
• Dimensional advantage in secure information trading via the noisy dense coding protocol
• Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols
• Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography
• Towards Necessary and sufficient state condition for violation of a multi-settings Bell inequality
• Provable entanglement and information cost for qubit-based quantum key-distribution protocols
• Robustness of the BB84 quantum key distribution protocol against general coherent attacks
• Quantum Sampling for Optimistic Finite Key Rates in High Dimensional Quantum Cryptography