Experimental investigation of quantum uncertainty relations with classical shadows
arXiv:2202.06441 · doi:10.3389/fphy.2022.873810
Abstract
The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum uncertainty relations construed with relative entropy of coherence, norm of coherence and coherence of formation. In stead of quantum state tomographic technology, we employ the classical shadow algorithm for the detection of lower bounds in quantum uncertainty relations. With an all optical setup, we prepare a family of quantum states whose purity can be fully controlled. We experimentally explore the tightness of various lower bounds in different reference bases on the prepared states. Our results indicate the tightness of quantum coherence lower bounds dependents on the reference bases as well as the purity of quantum state.
arXiv comment6 pages, 5 figures
References in corpus (34)
- Quantum entanglement
- Advances in Quantum Metrology
- Quantifying Coherence
- Quantum Coherence as a Resource
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Operational Resource Theory of Coherence
- The Uncertainty Principle in the Presence of Quantum Memory
- Entropic Uncertainty Relations and their Applications
- Probing entanglement entropy via randomized measurements
- The Uncertainty Relation for Smooth Entropies
- Intrinsic randomness as a measure of quantum coherence
- Frozen Quantum Coherence
- Mixed-state entanglement from local randomized measurements
- EPR Steering Inequalities from Entropic Uncertainty Relations
- Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
- Experimental investigation of the uncertainty principle in the presence of quantum memory
- Experimental investigation of the entanglement-assisted entropic uncertainty principle
- Duality of Quantum Coherence and Path Distinguishability
- Quantum Randomness Certified by the Uncertainty Principle
- Coherence depletion in the Grover quantum search algorithm
- Source-independent quantum random number generation
- Measure-Independent Freezing of Quantum Coherence
- Information theoretic treatment of tripartite systems and quantum channels
- Quantum uncertainty relation using coherence
- An equality between entanglement and uncertainty
- Quantum and classical entropic uncertainty relations
- Experimental quantum state measurement with classical shadows
- Unification of different views of decoherence and discord
- Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
- Operational interpretation of coherence in quantum key distribution
- Experimental investigation of entropic uncertainty relations and coherence uncertainty relations
- Quantum Coherence and Intrinsic Randomness
- Coherence Depletion in Quantum Algorithms
- Efficient estimation of multipartite quantum coherence