A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

A single qubit driven by an appropriate sequence of control pulses can serve as a spectrometer of local noise affecting its energy splitting. We show that by driving and observing two spatially separated qubits, it is possible to reconstruct the spectrum of cross-correlations of noises acting at various locations. When the qubits are driven by the same sequence of pulses, real part of cross-correlation spectrum can be reconstructed, while applying two distinct sequence to the two qubits allows for reconstruction of imaginary part of this spectrum. The latter quantity contains information on either causal correlations between environmental dynamics at distinct locations, or on the occurrence of propagation of noisy signals through the environment. We illustrate the former case by modeling the noise spectroscopy protocol for qubits coupled to correlated two-level systems. While entanglement between the qubits is not necessary, its presence enhances the signal from which the spectroscopic information is reconstructed.A qubit interacting with its environment experiences decoherence [1, 2] that limits the timescale on which it can be used for quantum information processing purposes. The time dependence of coherence decay is determined by dynamics of the environmental degrees of freedom coupled to the qubit. When the environment is well characterized, decoherence is simply a nuisance. On the other hand, when the dominant source of decoherence is unknown, measurements of qubit's coherence decay can be used to obtain substantial information about environmental fluctuations.Here we focus on the case in which the environment is a source of classical noise that affects the energy splitting of the qubits, i.e. it leads to pure dephasing. Driving the qubit with a sequence of dynamical decoupling (DD) pulses [3-10] not only slows down decoherence [11][12][13][14], but for an appropriately chosen (essentially periodic) sequence of n pulses, the magnitude of qubit's coherence at a given time t is proportional to spectral density of noise, S(ω), evaluated at ω = nπ/t [15][16][17][18][19]. Since the application of DD pulses to the qubit translates to modulating the phase noise with a periodic piece-wise constant function of alternating sign, this can be most easily understood as noise filtering by a lock-in mechanism [18].The efficacy of DD-based environmental noise spectroscopy (DDENS) with a single qubit was shown in many experiments on various kinds of qubits, including those based on trapped ions [11,18], superconducting circuits [15], semiconductor quantum dots [20,21], phosphorous donors in silicon [22], and NV centers in diamond [23,24]. It is crucial to note that in the case of solid-state based qubits, each qubit is interacting with a specific nanoscale environment, the exact properties of which vary from qubit to qubit. Furthermore, qubits tightly localized in a nanostructure (e.g. NV centers located close to a surface of a diamond nanocrystal), can * lcyw@ifpan.edu.pl be brought into contact with various environments, ...

We demonstrate that memory in an N -qubit system subjected to decoherence, is a potential resource for the slow-down of the entanglement decay. We show that this effect can be used to retain the sub shot-noise sensitivity of the parameter estimation in quantum interferometry. We calculate quantum Fisher information, which sets the ultimate bound for the precision of the estimation. We also derive the sensitivity of such a noisy interferometer, when the phase is either estimated from the measurements of the population imbalance or from the one-body density.

We investigate the properties of three-component Bose-Einstein condensate systems with spin exchange interactions. We consider different coupling constants from those very special ones leading to exact solutions known in the literature. When two solitons collide, a spin component oscillation of the two emerging entities is observed. This behavior seems to be generic. A mathematical model is derived for the emerging solitons. It describes the new oscillatory phenomenon extremely well. Surprisingly, the model is in fact an exact solution to the initial equations. This comes as a bonus.