Zero Uncertainty States in the Presence of Quantum Memory

Abstract

The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a quantum memory entangled with the system. Zero uncertainty states (in contrast with minimum uncertainty states) are peculiar quantum states that can eliminate uncertainties of incompatible von Neumann observables once assisted by suitable measurements on the memory. Here we determine all zero uncertainty states of any given set of nondegenerate observables and determine the minimum entanglement required. It turns out all zero uncertainty states are maximally entangled in a generic case, and vice versa, even if these observables are only weakly incompatible. Our work establishes a simple and precise connection between zero uncertainty and maximum entanglement, which is of interest to foundational studies and practical applications, including quantum certification and verification.

arXiv comment8+4 pages and two figures; title updated and published in npj Quantum Information

References in corpus (34)

• Quantum entanglement
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• The Uncertainty Principle in the Presence of Quantum Memory
• Remote State Preparation
• On mutually unbiased bases
• Entropic Uncertainty Relations and their Applications
• Tight Finite-Key Analysis for Quantum Cryptography
• Quantum Steering
• The Uncertainty Relation for Smooth Entropies
• Quantum steering: a review with focus on semidefinite programming
• Self-testing of quantum systems: a review
• Quantum certification and benchmarking
• Experimental investigation of the uncertainty principle in the presence of quantum memory
• Experimental investigation of the entanglement-assisted entropic uncertainty principle
• Optimal Remote State Preparation
• Quantum root-mean-square error and measurement uncertainty relations
• Uncertainty relations from simple entropic properties
• One-to-one mapping between steering and joint measurability problems
• Negativity and steering: a stronger Peres conjecture
• Experimental Verification of Multipartite Entanglement in Quantum Networks
• Optimal verification of entangled states with local measurements
• Efficient Verification of Pure Quantum States in the Adversarial Scenario
• Noise Robustness of the Incompatibility of Quantum Measurements
• A study of LOCC-detection of a maximally entangled state using hypothesis testing
• General framework for verifying pure quantum states in the adversarial scenario
• Robustness of incompatibility for quantum devices
• Operator monotones, the reduction criterion and the relative entropy
• Self-testing through EPR-steering
• Optimal verification and fidelity estimation of maximally entangled states
• A measure of physical reality
• Information-reality complementarity: The role of measurements and quantum reference frames
• Coherence and entanglement measures based on Rényi relative entropies
• Uncertainty from Heisenberg to Today
• Uncertainty-Reality Complementarity and Entropic Uncertainty Relations

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• Optimal Verification of the Bell State and Greenberger-Horne-Zeilinger States in Untrusted Quantum Networks