Entanglement sampling and applications

Abstract

A natural measure for the amount of quantum information that a physical system E holds about another system A = A_1,...,A_n is given by the min-entropy Hmin(A|E). Specifically, the min-entropy measures the amount of entanglement between E and A, and is the relevant measure when analyzing a wide variety of problems ranging from randomness extraction in quantum cryptography, decoupling used in channel coding, to physical processes such as thermalization or the thermodynamic work cost (or gain) of erasing a quantum system. As such, it is a central question to determine the behaviour of the min-entropy after some process M is applied to the system A. Here we introduce a new generic tool relating the resulting min-entropy to the original one, and apply it to several settings of interest, including sampling of subsystems and measuring in a randomly chosen basis. The sampling results lead to new upper bounds on quantum random access codes, and imply the existence of "local decouplers". The results on random measurements yield new high-order entropic uncertainty relations with which we prove the optimality of cryptographic schemes in the bounded quantum storage model.

v3: fixed some typos, v2: fixed minor issue with the definition of entropy and improved presentation

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• Advances in Quantum Cryptography
• Entropic Uncertainty Relations and their Applications
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• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Quantum Cryptography Beyond Quantum Key Distribution
• Entropy accumulation
• Decoupling with random quantum circuits
• Renyi generalizations of the conditional quantum mutual information
• Entropic uncertainty and measurement reversibility
• Optimized entropic uncertainty relations for multiple measurements
• Quantum algorithm for Petz recovery channels and pretty good measurements
• Quantum Achievability Proof via Collision Relative Entropy
• Tightening the tripartite quantum memory assisted entropic uncertainty relation
• Device-independent two-party cryptography secure against sequential attacks
• Applications of position-based coding to classical communication over quantum channels
• Renyi relative entropies of quantum Gaussian states
• Continuous-Variable Protocol for Oblivious Transfer in the Noisy-Storage Model
• Pretty good measures in quantum information theory
• Device-independence for two-party cryptography and position verification
• The holographic entropy zoo
• Entropic uncertainty relations with quantum memory in a multipartite scenario
• Entanglement witness and entropy uncertainty of open Quantum systems under Zeno effect
• Entropic uncertainty relations for SIC-POVMs and MUMs
• Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector
• Quantum preparation uncertainty and lack of information
• Entanglement and entropy uncertainty in black hole quantum atmosphere
• Universal security for randomness expansion from the spot-checking protocol
• Error-tolerant oblivious transfer in the noisy-storage model
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• Sampled sub-block hashing for large input randomness extraction
• Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario
• Loss of Information in Quantum Guessing Game
• General framework of quantum complementarity from a measurement-based perspective
• Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices
• The reduction of entropy uncertainty for qutrit system under non-Markov noisy environment
• Quantum Universally Composable Oblivious Linear Evaluation
• Uncorrelated problem-specific samples of quantum states from zero-mean Wishart distributions
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases
• The dynamics of entropy uncertainty for qutrit system under the random telegraph noise