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.

8+4 pages and two figures; title updated and published in npj Quantum Information

References in corpus (8)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Quantum certification and benchmarking
• Optimal Remote State Preparation
• Experimental Verification of Multipartite Entanglement in Quantum Networks
• Efficient Verification of Pure Quantum States in the Adversarial Scenario
• General framework for verifying pure quantum states in the adversarial scenario
• Coherence and entanglement measures based on Rényi relative entropies
• Uncertainty from Heisenberg to Today

Cited by in corpus (4)

• Quantum Measurements in the Light of Quantum State Estimation
• Quantum observable's reality erasure with spacelike-separated operations
• Correlating Local Quantum Reality with Causally Disconnected Choices
• Optimal Verification of the Bell State and Greenberger-Horne-Zeilinger States in Untrusted Quantum Networks