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We study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\mathcal N: \mathbb C^{d_{\mathrm{in}} \times d_{\mathrm{in}}} \to \mathbb C^{d_{\mathrm{out}} \times d_{\mathrm{out}}}$ in diamond norm distance requires $\Omega(\sqrt{d_{\mathrm{in}}} / \varepsilon)$ queries, even in the strongest algorithmic model that admits ancillae, coherence, and adaptivity. This is due to the worst-case nature of the distance induced by the diamond norm. Motivated by this limitation and other theoretical and practical applications, we introduce an average-case analogue of the diamond norm, which we call the average-case imitation diamond (ACID) norm. In the weakest algorithmic model without ancillae, coherence, or adaptivity, we prove that testing identity to certain types of channels in ACID distance can be done with complexity independent of the dimensions of the channel, while for other types of channels the complexity depends on both the input and output dimensions. Building on previous work, we also show that identity to any fixed channel can be tested with $\tilde O(d_{\mathrm{in}} d_{\mathrm{out}}^{3/2} / \varepsilon^2)$ queries in ACID distance and $\tilde O(d_{\mathrm{in}}^2 d_{\mathrm{out}}^{3/2} / \varepsilon^2)$ queries in diamond distance in this model. Finally, we prove tight bounds on the complexity of channel tomography in ACID distance.

We investigate the precision of estimating the interaction strength between a two-level system (TLS) and a single-photon pulse when the latter is subject to chirping. We consider linear, quadratic, and sinusoidal temporal phases applied to Gaussian and exponential temporal profiles. At the asymptotic time, when the TLS has fully decayed to its ground state, the fundamental precision depends solely on the magnitude of its spectral amplitude. For quadratically phase-modulated Gaussian pulses, this is entirely determined by the spectral bandwidth. We provide expressions for evaluating the fundamental precision for general temporal profiles and phase modulations. Finally, we show that experimentally feasible mode-resolved measurements are optimal, or close to it, for chirped, pulsed single photon spectroscopy.

Quantum vacuum fluctuations of the electromagnetic field result in two signatures on a harmonically trapped charged particle: a shift from the natural trap frequency and generation of quantum coherences. We assess the role of the long-wavelength and rotating-wave approximations in estimating this frequency shift. We estimate the magnitude of the frequency shift using parameters from a single-electron cyclotron experiment and also demonstrate how the dependence of the frequency shift on the magnetic field of the cyclotron is tied to the rotating-wave approximation. We expect the frequency shift to be observable in future experiments. We also suggest a possible route to detecting vacuum-generated quantum coherences. These experiments should settle the debate on the choice of approximations and gauge in capturing the effect of the quantum vacuum fluctuations., Comment: 6 pages, 1 figure

To investigate the transport properties in random alloys, it is important to model the alloy disorder using supercells. Though traditional methods like Virtual Crystal Approximation (VCA) are computationally efficient, the local disorder in the system is not accurately captured as artificial translational symmetry is imposed on the system. However, in the case of supercells, the error introduced by self-image interaction between the impurities is reduced and translational symmetry is explicitly imposed over larger length scales. In this work, we have investigated the Effective Phonon Dispersion (EPD) and transport properties, from first principle calculations using supercells in AlxGa1-xN alloy systems. Using our in-house developed code, the EPD of AlGaN is obtained and the individual modes are identified. Next, we discuss our in-house developed method to calculate low-field transport properties in supercells. First to validate our methods we have solved the Boltzmann Transport Equation using Rode method to compare the phonon limited mobility in the 4 atom GaN primitive cell and 12 atom GaN supercell. Using the same technique, we have investigated the low field transport in random AlxGa1-xN alloy systems. Our calculations show that along with alloy scattering, electron-phonon scattering may also play an important role at room temperature and high-temperature device operation. This technique opens up the path for calculating phonon-limited transport properties in random alloy systems.