Abstract

Quantum experiments that involve post-selection or filtering have generated heated debate over the last decades— from a foundational and a practical perspective. Pre- and post-selected expectation values of a weakly measured observable can lie outside an observable’s eigenspectrum. Classical theories cannot explain this. In this talk, I investigate post-selection within the framework of single- and multi-parameter quantum learning.

Quantum learning (in metrology and machine learning) involves estimating unknown parameters 𝜽 = (𝜃_1, 𝜃_2,… , 𝜃_𝑀) from measurements of quantum states 𝜌_𝜽. The quantum Fisher information matrix can bound the average amount of information learnt about 𝜽 per experimental trial. In several scenarios, it is advantageous to concentrate information in as few states as possible, for example, to avoid detector saturation. Here, we present a “go-go” theorem proving the possibility of unbounded and lossless distillation of Fisher information about multiple parameters in quantum learning. That is, there is no cap on how much quantum information can be distilled into a subset of quantum particles. My, and collaborators’, results enable the construction of filters that can reduce arbitrarily the number of quantum states, whilst retaining all initial information. The fundamental resource underlying this unbounded information distillability, I will show, is Kirkwood-Dirac negativity, a narrower non-classicality concept than non-commutation.

The recipe for lossless and unbounded distillation of quantum information, extends pre- and post-selected techniques of weak-value amplification to the growing fields of quantum machine learning and quantum metrology. If time permits, I will describe a proof-of-principle experiment where collaborators and I demonstrate how the use of quantum-filtering can boost the information content of single photons about an unknown polarisation rotation by a factor of over 200.

References: [1] https://www.nature.com/articles/s41467-020-17559-w [2] https://arxiv.org/abs/1811.08046 [3] https://arxiv.org/abs/2111.01194 [4] https://iopscience.iop.org/article/10.1088/1751-8121/ac0289