# 2021

**Convergence rates for the quantum central limit theorem**, S. Becker, N. Datta, L. Lami, and C. Rouzé, Commun. Math. Phys. 383 (2021) 223–279

DOI: https://doi.org/10.1007/s00220-021-03988-1

#### The gist of it

Suppose that you have a long optical fibre, over which you try to send a quantum message. The fibre is immersed in a noisy environment (possibly including other active components of your quantum circuit), and occasionally a photon coming from it can make its way into the fibre and disturb the transmitted signal. How can we model the overall process? A celebrated “quantum central limit theorem” due to Cushen and Hudson implies that in the limit where the number n of i.i.d. elementary interactions with the environment tends to infinity the overall process amounts to a very simple thermal attenuator, under very general assumptions on the environment’s state. But how fast does this convergence take place? Here we prove, among other things, that the Hilbert-Schmidt norm distance between the effective environment state and the thermal state tends to zero at a rate inversely proportional to the square root of n, whenever the third moments of the initial environment’s state are finite. Via analytical and numerical examples we show that our results are tight in many respects. This allows us to establish bounds on the classical and quantum capacities of the quantum channel modelling the above optical fibre.

**Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem**, S. Becker, N. Datta, L. Lami, and C. Rouzé, Phys. Rev. Lett. 126, 190504,

DOI: https://doi.org/10.1103/PhysRevLett.126.190504

#### The gist of it

How much energy do you need to discriminate two unitary quantum channels? And how much entanglement? Here we investigate these questions and establish a number of results. First, we prove that optimal discrimination between two unitary channels in the presence of an energy constraint does not require the use of any entanglement. In practice, this means that the resources needed to achieve optimal discrimination are substantially reduced. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this energy-constrained setting. Secondly, we employ mathematical tools known as energy-constrained diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. These results answer the question of how fast one can guess the Hamiltonian a system is subjected to given its initial mean energy. Thirdly, we establish a version of the Solovay-Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the energy-constrained diamond norm relative to the photon number Hamiltonian. This theorem allows us to efficiently compile continuous variable quantum circuits.

**Coherence of operations and interferometry**, M. Masini, T. Theurer, and M. B. Plenio, Phys. Rev. A 103, 042426

DOI: doi.org/10.1103/PhysRevA.103.042426

#### The gist of it

Quantum coherence is at the core of many quantum properties that are believed to lead to quantum advantages in fields such as computation, communication, simulation, and sensing. Therefore, it is considered a resource and characterized with the help of quantum resource theories. An application of the resulting framework to concrete technological tasks is however non-trivial and largely missing. In this work, we address this gap and connect how well operations can detect or create coherence (as quantified from a resource theoretical perspective) to the performance of interferometric experiments that rely on these operations.

**Ground-State Cooling of Levitated Magnets in Low-Frequency Traps**, K. Streltsov, J. S. Pedernales, and M. B. Plenio, Phys. Rev. Lett. 126, 193602

DOI: doi.org/10.1103/PhysRevLett.126.193602

#### The gist of it

The ability to operate massive particles in the quantum regime is predicted to bring exceptional enhancements in sensitivity for metrological applications, and enable fundamental tests of the nature of the gravitational interaction. Such control can be reached via cooling the particles to their quantum mechanical ground state. With increasing mass this turns into a progressively harder task. In this work we present a feedback cooling scheme that is capable of reaching the ground state of trapped magnetic particles with radii in the range of 1-10um.

**Framework for resource quantification in infinite-dimensional general probabilistic theories**, L. Lami, B. Regula, R. Takagi, and G. Ferrari, Phys. Rev. A 103, 032424

DOI: doi.org/10.1103/PhysRevA.103.032424

#### The gist of it

It is well established that several features of quantum mechanical systems with no classical counterparts can be exploited as resources in practical applications, such as communication, computation, sensing and cryptography. It is then of paramount importance to rigorously quantify such an advantage, especially in relation to some explicit task that one might want to perform in a realistic scenario. In these two papers, we study the (generalized) robustness as a measure of a very large family of generic quantum resources, and its relation with a key task in quantum information: quantum channel discrimination. In particular, we prove that the robustness precisely quantifies the maximum advantage given by a resourceful state with respect to any free one, when used as a probe to determine which physical evolution it underwent. Our framework can be applied well beyond standard finite-dimensional quantum theory, and in particular, to all finite- and infinite-dimensional general probabilistic theories, i.e., generalizations of quantum mechanics itself. This is interesting both from a fundamental and practical perspective, as many resources needed for quantum technologies, e.g. nonclassicality and non-Gaussianity, are peculiar of systems with an associated infinite-dimensional Hilbert space.

**Operational Quantification of Continuous-Variable Quantum Resources**, B. Regula, L. Lami, G. Ferrari, and R. Takagi, Phys. Rev. Lett. 126, 110403,

DOI: doi.org/10.1103/PhysRevLett.126.110403

#### The gist of it

It is well established that several features of quantum mechanical systems with no classical counterparts can be exploited as resources in practical applications, such as communication, computation, sensing and cryptography. It is then of paramount importance to rigorously quantify such an advantage, especially in relation to some explicit task that one might want to perform in a realistic scenario. In these two papers, we study the (generalized) robustness as a measure of a very large family of generic quantum resources, and its relation with a key task in quantum information: quantum channel discrimination. In particular, we prove that the robustness precisely quantifies the maximum advantage given by a resourceful state with respect to any free one, when used as a probe to determine which physical evolution it underwent. Our framework can be applied well beyond standard finite-dimensional quantum theory, and in particular, to all finite- and infinite-dimensional general probabilistic theories, i.e., generalizations of quantum mechanics itself. This is interesting both from a fundamental and practical perspective, as many resources needed for quantum technologies, e.g. nonclassicality and non-Gaussianity, are peculiar of systems with an associated infinite-dimensional Hilbert space.

**Parallel selective nuclear-spin addressing for fast high-fidelity quantum gates**, B. Tratzmiller, J. F. Haase, Z. Wang, and M. B. Plenio, Phys. Rev. A 103, 012607

DOI: doi.org/10.1103/PhysRevA.103.012607

#### The gist of it

Due to their long coherence times, nuclear spins have gained considerable attention as physical qubits. Their interaction can be mediated by nitrogen vacancy (NV) centers in diamond. In this work we generalize PulsePol, a pulse sequence developed in the Institute of Theoretical Physics to achieve robust polarization transfer from NV centers to nuclear spins, to a sequence that is resonant to two frequencies simultaneously, allowing to perform gates between two nuclear spins.

This approach results in efficient entangling gates that, compared to standard techniques, reduce the gate time by more than 50% when the gate time is limited by off-resonant coupling to other spins, and by up to 22% when the gate time is limited by small electron-nuclear coupling.

**Precise Spectroscopy of High-Frequency Oscillating Fields with a Single-Qubit Sensor**, Y. Chu, P. Yang, M. Gong, M. Yu, B. Yu, M. B. Plenio, A. Retzker, and J. Cai, Phys. Rev. Applied 15, 014031

DOI: doi.org/10.1103/PhysRevApplied.15.014031

#### The gist of it

In recent years our group has been interested in the application of NV centers for the detection of weak classical or quasi-classical fields. In our earlier works (e.g. Schmitt et al, Science 2017) we had been interested in the detection of fields due to the precession of nuclear spins in an external magnetic field which finds application in NMR. Such fields oscillate in the MHz regime, but there is also considerable interest in the detection of fields in the GHz regime, that is microwaves. To achieve this, the pulsed schemes of our earlier works are hard to realise at sufficient rates so that we had to change the detection protocol employing continuous control fields, much in the spirit of optical heterodyne detection, that enable the comparison of the known driving field with the unknown high frequency signal field.

# News

Julen Pedernales did it again, Best Post Prize at the UniKORN Poster Session 2021

Martin Plenio is listed as highly cited researcher for the fourth time in a row.

Our work on Quantum Physics and Biology featured Local and National Radio

Ludovico Lami wins a Humboldt Fellowship to continue his work in our group for another 2 years

# Most Recent Papers

**Convergence rates for the quantum central limit theorem**, Commun. Math. Phys. 383 (2021) 223–279

**Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem**, Phys. Rev. Lett. 126, 190504

**Coherence of operations and interferometry**, Phys. Rev. A 103, 042426

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