Seminars

Wheeler’s delayed-choice experiment, a scenario wherein a classical apparatus, typically an interferometer, is settled only after the quantum system has entered it, has corroborated the complementarity principle. However, the quantum version of Wheeler’s delayed-choice experiment has challenged the robustness of this principle. Based on the visibility at the output of a quantum-controlled interferometer, a conceptual framework has been put forward which detaches the notions of wave and particle from the quantum state.
In this talk, I will present our results concerning a quantum-controlled reality experiment, a slightly modified setup that is based on exchanging the causal order between the two main operations of the quantum Wheeler’s delayed-choice arrangement. We employed an operational criterion of physical realism to reveal a different state of affairs concerning the wave-and-particle behavior in this new setup. An experimental proof-of-principle will be presented for a two-spin-1/2 system in an interferometric setup implemented in a nuclear magnetic resonance platform. Finally, it will be discussed how our results validate the complementarity principle.

We introduce a family of positive linear maps in the algebra of 3 x3 complex matrices, which generalizes the seminal positive non-decomposable map originally proposed by Choi. Necessary and sufficient conditions for decomposability are derived and demonstrated. The proposed maps offer a new method for the analysis of bound entangled states of two qutrits.

Based on: https://arxiv.org/abs/2212.03807

In this work, we report a deterministic and exact algorithm to reverse any unknown qubit-encoding isometry operation. We present the semidefinite programming (SDP) to search the Choi matrix representing a quantum circuit reversing any unitary operation. We derive a quantum circuit transforming four calls of any qubit-unitary operation into its inverse operation by imposing the SU(2)×SU(2) symmetry on the Choi matrix. This algorithm only applies only for qubit-unitary operations, but we extend this algorithm to any qubit-encoding isometry operations. For that, we derive a subroutine to transform a unitary inversion algorithm to an isometry inversion algorithm by constructing a quantum circuit transforming finite sequential calls of any isometry operation into random unitary operations.

Recently it was shown, in the three-dimensional Anderson model [1] and the avalanche model of ergodicity breaking transitions [2], that the spectral form factor and the Thouless time extracted from the spectral form factor are scale invariant quantities at eigenstate transition. Thus they represent useful measures for characterisation of eigenstate transition. In the literature, an alternative definition of the Thouless time was given in terms of survival probability [3,4] which measure the stability of an initial state. Motivated by this fact, we investigate the survival probability measure and possible connections to the spectral form factor measure.

We focus on differences in behavior of the survival probability across the eigenstate transitions. Remarkably, we observe scaling invariant power-law decay of the survival probability at the transition in three physically relevant models: the three-dimensional Anderson model, one-dimensional Aubry-Andre model, and the avalanche model of ergodicity breaking transitions. We discuss connections of this universality to the universality of the spectral form factor measure. Our study [5] demonstrate that both quantities, the survival probability and the spectral form factor, are useful tool for detection of the eigenstate transitions.

[1] J. Šuntajs, T. Prosen and L. Vidmar, Annals of Physics 435, 168469 (2021)

[2] J. Šuntajs and L. Vidmar, Phys. Rev. Lett. 129, 060602 (2022)

[3] M. Schiulaz, E. J. Torres-Herrera, and L. F. Santos, Phys. Rev. B 99, 174313 (2019)

[4] T. L. M. Lezama, E. J. Torres-Herrera, F. Pérez-Bernal, Y. Bar Lev, and L. F. Santos, Phys. Rev. B 104, 085117 (2021)

[5] M. Hopjan and L. Vidmar, ArXiv:2212.13888