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# Manipulate coherent quantum states by measurements

*Published on 18 January 2024*

All physicists are taught that quantum measurements destroy coherence. Yet, if performed with care they can preserve coherence and even manipulate quantum states.

The researchers from PHELIQS/GT [**Collaboration**] investigated geometric phases induced by quantum measurements and found that these may behave in drastically (topologically) different ways under protocols employing strong or weak measurements. For weak measurements (small measurement strength: η→0; η=0.2 in Fig. 1), the qubit hardly changes its state and thus acquires little geometric phase; for strong measurements (η→∞; η=0.7 in Fig. 1), the qubit state follows extended trajectories and acquires significant geometric phase. It turns out that this distinction is not only quantitative but can be qualitative.

One can plot the dependence of the geometric phase χ on the protocol parameter θ on a torus with the two respective coordinates (Fig. 2). The curve for weak measurement winds around the horizontal circle on a torus, but not around the vertical one. The curve for strong measurements winds around both. A continuous deformation cannot transform one curve into another, making them topologically distinct. This automatically implies that the transition between the two behaviours is abrupt, occurring at some intermediate measurement strength.

The work has started with a number of theoretical investigations:

- see ref.[1]
*PNAS*2020 - see ref.[2]
*Phys.Rev.Lett.*2021 - see ref [3]
*Phys.Rev.Research*2021 (the most comprehensive one and recommended for learning the topic).

And now it has culminated in experimental verification of the predictions:

- in a superconducting qutrit (see ref.[4]
*Phys.Rev.Research*2022) - in an optical platform (see ref.[5]
*Science Advances*2023)

It is hard to foresee specific applications resulting from the above works on the topological transitions of measurement-induced geometric phases. Yet these contribute to our knowledge of how quantum systems affected by their decohering environment behave. This knowledge may be valuable, in particular, when trying to perform simulations of real-world materials using quantum simulators – which are subject to decoherence/measurements by their environment.

**Figure 1:**Measurements of different strength (η) affect the system’s quantum state (black dots connected by arrows showing the state change due to quantum measurements) in different ways. Weaker measurements hardly make the state move (η=0.2) while stronger measurements (η=0.7) force the system to change its state significantly. The area of the state trajectory (blue) determines the geometric phase and is also clearly different depending on the measurement strength. (Based on a figure from ref.[5] Science Advances 2023).

**Figure 2:**The weaker and stronger measurements lead to topologically distinct geometric phase behaviours: winding or not winding around the vertical cycle of the torus. (Based on a figure from ref.[5] Science Advances 2023).

**Collaboration:**the Weizmann Institute of Science (Israel), University of Freiburg (Germany), Lancaster University (UK), Washington University in St. Louis (USA), and University of Ottawa (Canada).