A de Finetti representation theorem for infinite dimensional quantum systems and applications to quantum cryptography

Abstract

According to the quantum de Finetti theorem, if the state of an N-partite system is invariant under permutations of the subsystems then it can be approximated by a state where almost all subsystems are identical copies of each other, provided N is sufficiently large compared to the dimension of the subsystems. The de Finetti theorem has various applications in physics and information theory, where it is for instance used to prove the security of quantum cryptographic schemes. Here, we extend de Finetti's theorem, showing that the approximation also holds for infinite dimensional systems, as long as the state satisfies certain experimentally verifiable conditions. This is relevant for applications such as quantum key distribution (QKD), where it is often hard - or even impossible - to bound the dimension of the information carriers (which may be corrupted by an adversary). In particular, our result can be applied to prove the security of QKD based on weak coherent states or Gaussian states against general attacks.

11 pages, LaTeX

References in corpus (8)

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Cited by in corpus (21)

• Finite-size analysis of continuous-variable quantum key distribution
• Composable security proof for continuous-variable quantum key distribution with coherent states
• Security of continuous-variable quantum key distribution against general attacks
• Coexistence of continuous variable QKD with intense DWDM classical channels
• Field test of a continuous-variable quantum key distribution prototype
• Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier
• Entanglement of Gaussian states and the applicability to quantum key distribution over fading channels
• Asymptotic security of continuous-variable quantum key distribution with a discrete modulation
• Continuous-Variable Quantum Key Distribution with Entanglement in the Middle
• Gaussian Post-selection for Continuous Variable Quantum Cryptography
• Reverse Reconciliation Continuous Variable Quantum Key Distribution Based on the Uncertainty Principle
• Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration
• Long-distance continuous-variable measurement-device-independent quantum key distribution with discrete modulation
• Continuous-variable quantum key distribution with Gaussian source noise
• Enhancement of the security of a practical continuous-variable quantum-key-distribution system by manipulating the intensity of the local oscillator
• Noiseless Linear Amplifiers in Entanglement-Based Continuous-Variable Quantum Key Distribution
• Numerical simulation of the optimal two-mode attacks for two-way continuous-variable quantum cryptography in reverse reconciliation
• Effect of Intensity Modulator Extinction on Practical Quantum Key Distribution System
• Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
• Continuous-variable measurement-device-independent quantum key distribution via quantum catalysis
• Non-Markovian Reactivation of Quantum Relays