“All in one” tests of quantum states

A collaboration between Armin Tavakoli - postdoc at IQOQI Vienna - and researchers the University of Science and Technology of China, has shown that data collected in a single experiment can be used to robustly certify the entanglement of a quantum system under several different assumptions, all at once. The work, recently published in Physical Review Letters, is a step towards developing flexible quantum information protocols that can simultaneously perform multiple different tasks.

A shared quantum state can be certified by performing local measurements that are either uncharacterized (black-box) or characterized (white-box). Depending on the selected assumptions, increasingly strong entanglement detection criteria can be constructed, at the cost of requiring more knowledge of the experimental setup.

Quantum theory beats the limits of classical physics in many different scenarios. When it comes to basic building blocks for today´s rapidly developing quantum technologies, three instances of nonclassicality are particularly distinguished. These are

  • Entanglement: when a quantum system cannot be understood by combining knowledge of its parts.

  • Steering: when a quantum system can display an “action at a distance” on a particle when another particle is measured.

  • Nonlocality: when a quantum system can be locally measured in such a way that no theory based on local physics can explain the results.

In order to detect entanglement, one performs a specific set of local measurements on each particle (white boxes) and uses the data to check for entanglement. In order to detect steering, one assumes control only of one measurement apparatus (white box), while the other measurement apparatus is viewed as an uncharacterized device (black box). Steering takes places from the untrusted devices to the trusted one. Finally, to detect nonlocality, one assumes that both measurement apparatuses are uncharacterized (black boxes) and nonlocality is asserted solely from the statistics they produce.

Entanglement, steering and nonlocality have each been the subject of intense study over many years. However, they typically require very different choices of measurement settings in order to successful be revealed. For instance, measuring two pairs of conjugate bases can sometimes reveal entanglement, but it can never reveal nonlocality. The recent publication finds a way to perform a test of nonlocality, steering, entanglement and even quantum state tomography, by only performing one experiment, i.e. one set of measurements on a shared state. In other words, the same experimental data can be recycled for several different purposes. By performing the designated measurements, one can first consider a complete black-box approach, i.e. a test of nonlocality. If that test fails, one can proceed to consider a test of steering, i.e. by assuming control of one device. If also that test fails, one can proceed further to consider a test of entanglement, i.e. by assuming control of both devices. The final tests allows one to completely reconstruct the underlying quantum state by means of quantum state tomography.

On the one hand, this ‘all in one’ method shows that different quantum features are more closely related than previously thought. On the other hand, it opens up a path for flexible experiments that can perform several different quantum tasks at once.


Original publication: “Nonlocality, steering and quantum state tomography in a single experiment”, Chang-Jiang Huang, Guo-Yong Xiang, Yu Guo, Kang-Da Wu, Bi-Heng Liu, Chuan-Feng Li, Guang-Can Guo and Armin Tavakoli, Phys. Rev. Lett. 127, 020401 (2021).