**Project OPUS IV of the National Science Centre entitled**

*“Dynamics of entanglement of localized spins in semiconductors with application to environmental noise spectroscopy” (2013-2017)
*

**Objectives**

The objective of the project is to develop theoretical understanding of entanglement dynamics and its control in systems consisting of multiple spin qubits. Entanglement is a unique property of composite quantum systems: entangled states exhibit nonlocal correlations among the subsystems that cannot be described classically. The ability to create, store, and manipulate entangled states is crucial for practically all the envisioned technologies using truly quantum aspects of physical systems. Recently entanglement was created among spins in a semiconductor environment. Architectures involving such spin qubits are considered to have a high potential for scalability, necessary for creation of quantum circuits capable of nontrivial operations. The key theoretical problem that we will research is the interaction of multiple qubits with their solid-state environment (a spin bath and various sources of charge noise, both having long correlation times). We will also propose manipulation schemes making it possible to obtain information about environmental noise from measurements of qubits’ dynamics – since the entangled qubits can be spatially separated, observation of their disentanglement can give information about not only temporal, but also spatial correlations of the noise.

**Main results obtained so far**

1) Theory of spectroscopy of cross-correlations of environmental noises using two (potentially entangled) qubits [6].

2) Theoretical description of decoherence under dynamical decoupling of two electrons in a double quantum dot (forming a singlet-triplet qubit) interacting with nuclear bath in GaAs [7,8].

3) Proposal of a method for determining the location of a precessing magnetic moment using two spin qubits [10].

4) Derivation of simple and intuitive criterion for checking whether qubit-environment entanglement is generated during pure dephasing decoherence of the qubit [5], and a follow-up discussion of qubit-environment discord generation [11].

5) Theory for using qubit as a noise spectrometer when the qubit is at so-called “optimal working point” and its coupling to the environmental noise is quadratic [1].

**Publications**

[12] D. Kwiatkowski and Ł. Cywiński

*Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: application to nitrogen vacancy centers*

Phys. Rev. B **98**, 155202 (2018)

arXiv:1806.06845

[11] K. Roszak and Ł. Cywiński

*Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the resulting consequences*

Phys. Rev. A **97**, 012306 (2018)

arXiv:1709.00558

[10] J. Krzywda, Ł. Cywiński, and P. Szańkowski

*Localization of a magnetic moment using a two-qubit probe*

Phys. Rev. A **96**, 042108 (2017)

arXiv:1706.02948

[9] P. Szańkowski, G. Ramon, J. Krzywda, D. Kwiatkowski, and Ł. Cywiński

*Environmental noise spectroscopy with qubits subjected to dynamical decoupling*

J. Phys.: Condens. Matter. **29**, 333001 (2017)

arXiv:1705.02262

[8] F. K. Malinowski, F. Martins, Ł. Cywiński, M. S. Rudner, P. D. Nissen, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, and F. Kuemmeth

*Spectrum of the Nuclear Environment for GaAs Spin Qubits*

Phys. Rev. Lett. **118**, 177702 (2017)

arXiv:1701.01855

[7] F. K. Malinowski, F. Martins, P. D. Nissen, E. Barnes, Ł. Cywiński, M. S. Rudner, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, and F. Kuemmeth

*Notch filtering the nuclear environment of a spin qubit
*Nature Nanotechnology

**12**, 16 (2017)

arXiv:1601.06677

[6] P. Szańkowski, M. Trippenbach, and Ł. Cywinski

*Spectroscopy of cross-correlations of environmental noises with two qubits*

Phys. Rev. A **94**, 012109 (2016)

arXiv:1507.03897

[5] K. Roszak and Ł. Cywiński

*Characterization and measurement of qubit-environment entanglement generation during pure dephasing*

Phys. Rev. A **92**, 032310 (2015)

arXiv:1506.05729

[4] K. Roszak and Ł. Cywiński

*The relation between the quantum discord and quantum teleportation: the physical interpretation of the transition point between different quantum discord decay regimes*

EPL **112**, 10002 (2015)

arXiv:1505.05741

[3] I. Bragar and Ł. Cywiński

*Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots*

Phys. Rev. B **91**, 155310 (2015)

arXiv:1411.6269

[2] P. Szańkowski, M. Trippenbach, Ł. Cywinski, and Y. B. Band

*The dynamics of two entangled qubits exposed to classical noise: role of spatial and temporal noise correlations*

Quantum Info. Process. **14**, 3367 (2015)

arXiv:1408.4254

[1] Ł. Cywiński

*Dynamical-decoupling noise spectroscopy at an optimal working point of a qubit*

Phys. Rev. A **90**, 042307 (2014)

arXiv:1308.3102