Determining quantum coherence with minimal resources
arXiv:1708.05597 · doi:10.1088/1367-2630/aacbea
Abstract
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a -level system, the optimal strategy consists of measuring orthonormal bases such that each measured basis is mutually unbiased with respect to the reference basis, and together with the reference basis they form an informationally complete set of measurements. We show that, in general, any strategy capable of validating quantum coherence allows one to evaluate also the exact value of coherence. We then give an explicit construction of the optimal measurements for arbitrary dimensions. Finally, we show that the same measurement setup is also optimal for the modified task of verifying if the coherence is above or below a given threshold value.
References in corpus (19)
- Quantifying Coherence
- Quantifying Entanglement
- Quantum Coherence as a Resource
- Operational Resource Theory of Coherence
- Measuring Quantum Coherence with Entanglement
- On mutually unbiased bases
- Robustness of coherence: An operational and observable measure of quantum coherence
- A new proof for the existence of mutually unbiased bases
- Observable measure of quantum coherence in finite dimensional systems
- Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
- Quantum-coherence quantifiers based on the Tsallis relative -entropies
- Entanglement and coherence in quantum state merging
- Towards resource theory of coherence in distributed scenarios
- Uniqueness of Quantum States Compatible with Given Measurement Results
- Logarithmic coherence: Operational interpretation of -norm coherence
- Tasks and premises in quantum state determination
- Verifying the quantumness of bipartite correlations
- Probing quantum state space: does one have to learn everything to learn something?
- Covariant mutually unbiased bases