Abstract
AbstractThe precision limit in quantum state tomography is of great interest not only to practical applications but also to foundational studies. However, little is known about this subject in the multiparameter setting even theoretically due to the subtle information trade-off among incompatible observables. In the case of a qubit, the theoretic precision limit was determined by Hayashi as well as Gill and Massar, but attaining the precision limit in experiments has remained a challenging task. Here we report the first experiment that achieves this precision limit in adaptive quantum state tomography on optical polarisation qubits. The two-step adaptive strategy used in our experiment is very easy to implement in practice. Yet it is surprisingly powerful in optimising most figures of merit of practical interest. Our study may have significant implications for multiparameter quantum estimation problems, such as quantum metrology. Meanwhile, it may promote our understanding about the complementarity principle and uncertainty relations from the information theoretic perspective.
Highlights
Quantum state tomography is a procedure for inferring the state of a quantum system from quantum measurements and data processing.[1,2,3]
The precision limit in quantum state tomography offers a perfect window for understanding the distinction between quantum physics and classical physics.[9,10,11,12]
In this work we report the first experiment that achieves the quantum precision limit in adaptive quantum state tomography on optical polarisation qubits
Summary
Quantum state tomography is a procedure for inferring the state of a quantum system from quantum measurements and data processing.[1,2,3] It is a primitive of various quantum information processing tasks such as quantum computation, communication, cryptography and metrology.[4,5,6,7,8] In sharp contrast with the classical world, any measurement on a generic quantum system necessarily induces a disturbance, limiting further attempts to extract information from the system. The precision limit in quantum state tomography offers a perfect window for understanding the distinction between quantum physics and classical physics.[9,10,11,12]. The tomographic precision limit in the multiparameter setting is still poorly understood; experimental studies are especially rare. To fill this gap, in this work we report the first experiment that achieves the quantum precision limit in adaptive quantum state tomography on optical polarisation qubits
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