Squash Operator and Symmetry

Abstract

This paper begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol which suits single-mode as well as multi-mode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C_4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of "rank two" can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.

4 pages, no figures; minor grammatical corrections

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• Decoy State Quantum Key Distribution
• Device-independent security of quantum cryptography against collective attacks
• Beating the PNS attack in practical quantum cryptography
• Device-independent quantum key distribution secure against collective attacks
• Lower and upper bounds on the secret key rate for QKD protocols using one--way classical communication
• Squashing Models for Optical Measurements in Quantum Communication
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Cited by in corpus (9)

• Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution
• Security proof for a simplified BB84-like QKD protocol
• Squashing model for detectors and applications to quantum key distribution protocols
• Dimension Reduction in Quantum Key Distribution for Continuous- and Discrete-Variable Protocols
• Estimating the photon-number distribution of photonic channels with realistic devices and applications in photonic quantum information processing
• Imperfect detectors for adversarial tasks with applications to quantum key distribution
• Multi-partite squash operation and its application to device-independent quantum key distribution
• Security loophole in error verification in quantum key distribution
• Security proofs for practical QKD: variations, techniques, gaps, and limitations