Hiding Ignorance Using High Dimensions

Abstract

The absence of information -- entirely or partly -- is called ignorance. Naturally, one might ask if some ignorance of a whole system will imply some ignorance of its parts. Our classical intuition tells us yes, however quantum theory tells us no: it is possible to encode information in a quantum system so that despite some ignorance of the whole, it is impossible to identify the unknown part arXiv:1011.6448. Experimentally verifying this counter-intuitive fact requires controlling and measuring quantum systems of high dimension $(d>9)$. We provide this experimental evidence using the transverse spatial modes of light, a powerful resource for testing high dimensional quantum phenomenon.

References in corpus (22)

• Review article: Linear optical quantum computing
• The Uncertainty Principle in the Presence of Quantum Memory
• On mutually unbiased bases
• Experimental high-dimensional two-photon entanglement and violations of generalised Bell inequalities
• The operational meaning of min- and max-entropy
• Entropic Uncertainty Relations and their Applications
• Tight Finite-Key Analysis for Quantum Cryptography
• Contextuality for preparations, transformations, and unsharp measurements
• High-Dimensional Intra-City Quantum Cryptography with Structured Photons
• The uncertainty principle determines the non-locality of quantum mechanics
• Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment
• An experimental test of noncontextuality without unwarranted idealizations
• Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes
• Cryptography from Noisy Storage
• Quantum Random Access Codes using Single $d$-level Systems
• Entropy and Information Causality in General Probabilistic Theories
• Optimal bounds for parity-oblivious random access codes
• Sampling of min-entropy relative to quantum knowledge
• High-dimensional quantum communication complexity beyond strategies based on Bell's theorem
• Continuous-Variable Protocol for Oblivious Transfer in the Noisy-Storage Model
• The Magical Number Seven: An Unexpected Dimensional Threshold in Quantum Communication Complexity
• Does ignorance of the whole imply ignorance of the parts? - Large violations of non-contextuality in quantum theory

Cited by in corpus (6)

• Robust and Efficient High-dimensional Quantum State Tomography
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• How many mutually unbiased bases are needed to detect bound entangled states?
• Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies
• Self-testing mutually unbiased bases in higher dimensions with space-division multiplexing optical fiber technology