Roland Krischek

Experimental entanglement of a six-photon symmetric Dicke state.

We augment the information extractable from a single absorption image of a spinor Bose-Einstein condensate by coupling to initially empty auxiliary hyperfine states. Performing unitary transformations in both the original and auxiliary hyperfine manifold enables the simultaneous measurement of multiple spin-1 observables. We apply this scheme to an elongated atomic cloud of ^{87}Rb to simultaneously read out three orthogonal spin directions and with that directly access the spatial spin structure. The readout even allows the extraction of quantum correlations which we demonstrate by detecting spin-nematic squeezing without state tomography.We report on the experimental observation and characterization of a six-photon entangled Dicke state. We obtain a fidelity as high as 0.654+/-0.024 and prove genuine six-photon entanglement by, amongst others, a two-setting witness yielding -0.422+/-0.148. This state has remarkable properties; e.g., it allows obtaining inequivalent entangled states of a lower qubit number via projective measurements, and it possesses a high entanglement persistency against qubit loss. We characterize the properties of the six-photon Dicke state experimentally by detecting and analyzing the entanglement of a variety of multipartite entangled states.

Fisher information and multiparticle entanglement

The Fisher information F gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on F for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information F for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on F is able to detect certain bound entangled states.

Permutationally Invariant Quantum Tomography

We present a scalable method for the tomography of large multiqubit quantum registers. It acquires information about the permutationally invariant part of the density operator, which is a good approximation to the true state in many relevant cases. Our method gives the best measurement strategy to minimize the experimental effort as well as the uncertainties of the reconstructed density matrix. We apply our method to the experimental tomography of a photonic four-qubit symmetric Dicke state.

Useful Multiparticle Entanglement and Sub-Shot-Noise Sensitivity in Experimental Phase Estimation

We experimentally demonstrate a general criterion to identify entangled states useful for the estimation of an unknown phase shift with a sensitivity higher than the shot-noise limit. We show how to exploit this entanglement on the examples of a maximum likelihood as well as of a Bayesian phase estimation protocol. Using an entangled four-photon state we achieve a phase sensitivity clearly beyond the shot-noise limit. Our detailed comparison of methods and quantum states for entanglement enhanced metrology reveals the connection between multiparticle entanglement and sub-shot-noise uncertainty, both in a frequentist and in a Bayesian phase estimation setting.

Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states

We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effort small. We also present general results on the efficient local decomposition of permutationally invariant operators, which makes it possible to measure projectors to symmetric states efficiently.

Multi-Photon Entanglement for Sub Shot-Noise Sensitivity

We experimentally demonstrate a general criterion to identify multi-photon entangled states useful for quantum metrology and prove their applicability for phase estimation with a sensitivity higher than the shot-noise limit.

Interferometric autocorrelation in the ultraviolet utilizing spontaneous parametric down-conversion inside an enhancement cavity

Autocorrelation is a common method to estimate the duration of ultrashort laser pulses. In the ultraviolet (UV) regime it is challenging to employ the process of second-harmonic generation, most prominently due to absorption in nonlinear crystals at very short wavelengths. Here we show how to utilize spontaneous parametric down-conversion (SPDC) to generate an autocorrelation signal in the infrared (IR) for UV pulses. Our method utilizes the nth-order emission of the SPDC process, which occurs for low pumping powers proportional to the nth power of the UV intensity. Thus, counting 2n down-converted photons directly yields the nth-order autocorrelation. The method, now with detection of near-IR photons, is applied to the first direct measurement of ultrashort UV pulses circulating inside a UV enhancement cavity.

Permutationally invariant tomography of a four-qubit symmetric Dicke state

Multi-partite entangled quantum states play an important role in quantum information processing with applications, for example, in quantum enhanced metrology or quantum communication. Therefore, efficient measurement schemes to fully characterize these states are needed. However, conventional quantum state tomography which reveals all properties of a quantum state suffers from an exponentially increasing measurement effort with the number of qubits.

Entanglement enhanced quantum sensing

Entanglement between quantum objects can be used to enhance the sensitivity of measurements. We demonstrate this effect by using entangled multi-photon states to go beyond the shot noise limit when observing polarization rotations.

Tunable Setup for an Entire Family of Four-Photon Entangled States

We report on the experimental observation and analysis of an entire family of four-photon entangled states. We demonstrate how these states can be obtained with a single linear optics set-up and analyze particular entanglement properties.