J. Sperling

Unified quantification of nonclassicality and entanglement

The nonclassicality of single-mode quantum states is studied in relation to the entanglement created by a beam splitter. It is shown that properly defined quantifications -- based on the quantum superposition principle -- of the amounts of nonclassicality and entanglement are strictly related to each other. This can be generalized to the amount of genuine multipartite entanglement, created from a nonclassical state by an N splitter. As a consequence, a single-mode state of a given amount of nonclassicality is fully equivalent, as a resource, to exactly the same amount of entanglement. This relation is also considered in the context of multipartite entanglement and multimode nonclassicality.

True photocounting statistics of multiple on-off detectors

We derive a closed photo-counting formula, including noise counts and a finite quantum efficiency, for photon number resolving detectors based on on-off detectors. It applies to detection schemes such as array detectors and multiplexing setups. The result renders it possible to compare the corresponding measured counting statistics with the true photon number statistics of arbitrary quantum states. The photo-counting formula is applied to the discrimination of photon numbers of Fock states, squeezed states, and odd coherent states. It is illustrated for coherent states that our formula is indispensable for the correct interpretation of quantum effects observed with such devices.

Full multipartite entanglement of frequency-comb Gaussian states.

An analysis is conducted of the multipartite entanglement for Gaussian states generated by the parametric down-conversion of a femtosecond frequency comb. Using a recently introduced method for constructing optimal entanglement criteria, a family of tests is formulated for mode decompositions that extends beyond the traditional bipartition analyses. A numerical optimization over this family is performed to achieve maximal significance of entanglement verification. For experimentally prepared 4-, 6-, and 10-mode states, full entanglement is certified for all of the 14, 202, and 115 974 possible nontrivial partitions, respectively.

Multipartite entanglement witnesses.

We derive a set of algebraic equations, the so-called multipartite separability eigenvalue equations. Based on their solutions, we introduce a universal method for the construction of multipartite entanglement witnesses. We witness multipartite entanglement of 10(3) coupled quantum oscillators, by solving our basic equations analytically. This clearly demonstrates the feasibility of our method for studying ultrahigh orders of multipartite entanglement in complex quantum systems.

The Schmidt number as a universal entanglement measure

The class of local invertible operations is defined, and the invariance of entanglement under such operations is established. For the quantification of entanglement, universal entanglement measures are defined, which are invariant under local invertible transformations. They quantify entanglement in a very general sense. It is shown that the Schmidt number is a universal entanglement measure, which is most important for the general amount of entanglement. For special applications, pseudo-measures are defined to quantify the entanglement useful for a certain quantum task. The entanglement quantification is further specified by operational measures, which include the observables accessible by a given experimental setup.

Sub-binomial light.

The click statistics from on-off detector systems is quite different from the counting statistics of the more traditional detectors. This necessitates the introduction of new parameters to characterize the nonclassicality of fields from measurements using on-off detectors. To properly replace the Mandel Q(M) parameter, we introduce a parameter Q(B). A negative value represents a sub-binomial statistics. This is possible only for quantum fields, even for super-Poisson light. It eliminates the problems encountered in discerning nonclassicality using Mandels Q(M) for on-off data.

Analytical progress on symmetric geometric discord: Measurement-based upper bounds

Quantum correlations may be measured by means of the distance of the state to the subclass ofstates having well defined classical properties. In particular, a geometric measure of asymmetricdiscord [Daki´c et al., Phys. Rev. Lett. 105, 190502 (2010)] was recently defined as the Hilbert-Schmidt distance of a given two-qubit state to the closest classical-quantum (CQ) correlated state.We analyze a geometric measure of symmetric discord defined as the Hilbert-Schmidt distance ofa given state to the closest classical-classical (CC) correlated state. The optimal member of isjust specially measured original state both for the CQ and CC discords. This implies that thismeasure is equal to quantum deficit of post-measurement purity. We discuss some general relationsbetween the CC discords and explain why an analytical formula for the CC discord, contrary to theCQ discord, can hardly be found even for a general two-qubit state. Instead of such exact formula,we find simple analytical measurement-based upper bounds for the CC discord which, as we show,are very efficient in the case of two qubits and may serve as independent indicators of two-partyquantum correlations. In particular, we propose an adaptive upper bound, which corresponds to theoptimal states induced by single-party measurements: optimal measurement on one of the partiesdetermines an optimal measurement on the other party. We discuss how to refine the adaptiveupper bound by nonoptimal single-party measurements and by an iterative procedure which usuallyrapidly converges to the CC discord. We also raise the question of optimality of the symmetricmeasurements realising the CC discord on symmetric states, and give partial answer for the qubitcase.

Quantum state engineering by click counting

We derive an analytical description for the quantum state preparation using systems of on-off detectors. Our method will apply the true click statistics of such detector systems. In particular, we consider heralded quantum state preparation using correlated light fields, photon addition and photon subtraction processes. Using a post-selection procedure to a particular number of clicks of the detector system, the output states reveal a variety of quantum features. The rigorous description allows the identification and characterization of fundamentally unavoidable attenuations within given processes. We also generalize a known scenario of noiseless amplification with click detectors for the purpose of the preparation of various types of nonclassical states of light. Our exact results are useful for the choice of experimental parameters to realize a target state.

Uncovering Quantum Correlations with Time-Multiplexed Click Detection

We report on the implementation of a time-multiplexed click detection scheme to probe quantum correlations between different spatial optical modes. We demonstrate that such measurement setups can uncover nonclassical correlations in multimode light fields even if the single mode reductions are purely classical. The nonclassical character of correlated photon pairs, generated by a parametric down-conversion, is immediately measurable employing the theory of click counting instead of low-intensity approximations with photoelectric detection models. The analysis is based on second- and higher-order moments, which are directly retrieved from the measured click statistics, for relatively high mean photon numbers. No data postprocessing is required to demonstrate the effects of interest with high significance, despite low efficiencies and experimental imperfections. Our approach shows that such novel detection schemes are a reliable and robust way to characterize quantum-correlated light fields for practical applications in quantum communications.

Representation of entanglement by negative quasiprobabilities

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously prove entanglement, their positivity proves separability.