Quantifying Measurement Incompatibility of Mutually Unbiased Bases.

Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k=d+1 MUB (using the standard construction for d being a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.

Simultaneous coherence enhancement of optical and microwave transitions in solid-state electronic spins.

Solid-state electronic spins are extensively studied in quantum information science, as their large magnetic moments offer fast operations for computing1 and communication2-4, and high sensitivity for sensing5. However, electronic spins are more sensitive to magnetic noise, but engineering of their spectroscopic properties, for example, using clock transitions and isotopic engineering, can yield remarkable spin coherence times, as for electronic spins in GaAs6, donors in silicon7-11 and vacancy centres in diamond12,13. Here we demonstrate simultaneously induced clock transitions for both microwave and optical domains in an isotopically purified 171Yb3+:Y2SiO5 crystal, reaching coherence times of greater than 100 µs and 1 ms in the optical and microwave domains, respectively. This effect is due to the highly anisotropic hyperfine interaction, which makes each electronic-nuclear state an entangled Bell state. Our results underline the potential of 171Yb3+:Y2SiO5 for quantum processing applications relying on both optical and spin manipulation, such as optical quantum memories4,14, microwave-to-optical quantum transducers15,16, and single-spin detection17, while they should also be observable in a range of different materials with anisotropic hyperfine interactions.

From quantum foundations to applications and back.

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

Robust Macroscopic Quantum Measurements in the Presence of Limited Control and Knowledge.

Quantum measurements have intrinsic properties that seem incompatible with our everyday-life macroscopic measurements. Macroscopic Quantum Measurement (MQM) is a concept that aims at bridging the gap between well-understood microscopic quantum measurements and macroscopic classical measurements. In this paper, we focus on the task of the polarization direction estimation of a system of N spins 1/2 particles and investigate the model some of us proposed in Barnea et al., 2017. This model is based on a von Neumann pointer measurement, where each spin component of the system is coupled to one of the three spatial component directions of a pointer. It shows traits of a classical measurement for an intermediate coupling strength. We investigate relaxations of the assumptions on the initial knowledge about the state and on the control over the MQM. We show that the model is robust with regard to these relaxations. It performs well for thermal states and a lack of knowledge about the size of the system. Furthermore, a lack of control on the MQM can be compensated by repeated "ultra-weak" measurements.

Experimental certification of millions of genuinely entangled atoms in a solid.

Quantum theory predicts that entanglement can also persist in macroscopic physical systems, albeit difficulties to demonstrate it experimentally remain. Recently, significant progress has been achieved and genuine entanglement between up to 2900 atoms was reported. Here, we demonstrate 16 million genuinely entangled atoms in a solid-state quantum memory prepared by the heralded absorption of a single photon. We develop an entanglement witness for quantifying the number of genuinely entangled particles based on the collective effect of directed emission combined with the non-classical nature of the emitted light. The method is applicable to a wide range of physical systems and is effective even in situations with significant losses. Our results clarify the role of multipartite entanglement in ensemble-based quantum memories and demonstrate the accessibility to certain classes of multipartite entanglement with limited experimental control.The presence of entanglement in macroscopic systems is notoriously difficult to observe. Here, the authors develop a witness which allow them to demonstrate entanglement between millions of atoms in a solid-state quantum memory prepared by the heralded absorption of a single photon.

Quantifying Photonic High-Dimensional Entanglement.

High-dimensional entanglement offers promising perspectives in quantum information science. In practice, however, the main challenge is to devise efficient methods to characterize high-dimensional entanglement, based on the available experimental data which is usually rather limited. Here we report the characterization and certification of high-dimensional entanglement in photon pairs, encoded in temporal modes. Building upon recently developed theoretical methods, we certify an entanglement of formation of 2.09(7) ebits in a time-bin implementation, and 4.1(1) ebits in an energy-time implementation. These results are based on very limited sets of local measurements, which illustrates the practical relevance of these methods.

High-Precision Measurement of the Dzyaloshinsky-Moriya Interaction between Two Rare-Earth Ions in a Solid.

We report on a direct measurement of the pairwise antisymmetric exchange interaction, known as the Dzyaloshinsky-Moriya interaction (DMI), in a Nd^{3+}-doped YVO_{4} crystal. To this end, we introduce a broadband electron spin resonance technique coupled with an optical detection scheme which selectively detects only one Nd^{3+}-Nd^{3+} pair. Using this technique we can fully measure the spin-spin coupling tensor, allowing us to experimentally determine both the strength and direction of the DMI vector. We believe that this ability to fully determine the interaction Hamiltonian is of interest for studying the numerous magnetic phenomena where the DMI interaction is of fundamental importance, including multiferroics. We also detect a singlet-triplet transition within the pair, with a highly suppressed magnetic-field dependence, which suggests that such systems could form singlet-triplet qubits with long coherence times for quantum information applications.

Detecting Large Quantum Fisher Information with Finite Measurement Precision.

We propose an experimentally accessible scheme to determine the lower bounds on the quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for quantum metrology. The scheme is based on comparing the measurement statistics of a state before and after a small unitary rotation. We argue that, in general, the limited resolution of collective observables prevents the detection of large QFI. This can be overcome by performing an additional operation prior to the measurement. We illustrate the power of this protocol for present-day spin-squeezing experiments, where the same operation used for the preparation of the initial spin-squeezed state improves also the measurement precision and hence the lower bound on the QFI by 2 orders of magnitude. We also establish a connection to the Leggett-Garg inequalities. We show how to simulate a variant of the inequalities with our protocol and demonstrate that large QFI is necessary for their violation with coarse-grained detectors.