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Register a new userEntanglement of a pair of quantum emitters via continuous fluorescence measurements: a tutorial
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We discuss recent developments in measurement protocols that generate quantum entanglement between two remote qubits, focusing on the theory of joint continuous detection of their spontaneous emission. We consider a device geometry similar to that used in well-known Bell-state measurements, which we analyze using a conceptually transparent model of stochastic quantum trajectories; we use this to review photodetection, the most straightforward case, and then generalize to the diffusive trajectories from homodyne and heterodyne detection as well. Such quadrature measurement schemes are a realistic two-qubit extension of existing circuit-QED experiments which obtain quantum trajectories by homodyning or heterodyning a superconducting qubits spontaneous emission, or an adaptation of existing optical measurement schemes to obtain jump trajectories from emitters. We mention key results, presented from within a single theoretical framework, and draw connections to concepts in the wider literature on entanglement generation by measurement (such as path information erasure and entanglement swapping). The photon which-path information acquisition, and therefore the two-qubit entanglement yield, is tunable under the homodyne detection scheme we discuss, at best generating equivalent average entanglement dynamics as in the comparable photodetection case. In addition to deriving this known equivalence, we extend past analyses in our characterization of the measurement dynamics: We include derivations of bounds on the fastest possible evolution towards a Bell state under joint homodyne measurement dynamics, and characterize the maximal entanglement yield possible using inefficient (lossy) measurements.
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We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubits state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and heterodyne monitoring, and illustrate its equivalence to the stochastic master equation formalism throughout. Special emphasis is given to homodyne (phase-sensitive) monitoring of fluorescence. The examples we develop are used to illustrate basic methods in quantum trajectories, but also to introduce some more advanced topics of contemporary interest, including the arrow of time in quantum measurement, and trajectories following optimal measurement records derived from a variational principle. The derivations we perform lead directly from the development of a simple model to an understanding of recent experimental results.
Solid-state quantum emitters are promising candidates for the realization of quantum networks, owing to their long-lived spin memories, high-fidelity local operations, and optical connectivity for long-range entanglement. However, due to differences in local environment, solid-state emitters typically feature a range of distinct transition frequencies, which makes it challenging to create optically mediated entanglement between arbitrary emitter pairs. We propose and demonstrate an efficient method for entangling emitters with optical transitions separated by many linewidths. In our approach, electro-optic modulators enable a single photon to herald a parity measurement on a pair of spin qubits. We experimentally demonstrate the protocol using two silicon-vacancy center sin a diamond nanophotonic cavity, with optical transitions separated by 7.4 GHz. Working with distinguishable emitters allows for individual qubit addressing and readout, enabling parallel control and entanglement of both co-located and spatially separated emitters, a key step towards scaling up quantum information processing systems
The unambiguous detection and quantification of entanglement is a hot topic of scientific research, though it is limited to low dimensions or specific classes of states. Here we identify an additional class of quantum states, for which bipartite entanglement measures can be efficiently computed, providing new rigorous results. Such states are written in arbitrary $dtimes d$ dimensions, where each basis state in the subsystem A is paired with only one state in B. This new class, that we refer to as pair basis states, is remarkably relevant in many physical situations, including quantum optics. We find that negativity is a necessary and sufficient measure of entanglement for mixtures of states written in the same pair basis. We also provide analytical expressions for a tight lower-bound estimation of the entanglement of formation, a central quantity in quantum information.
We present an experimental analysis of quadrature entanglement produced from a pair of amplitude squeezed beams. The correlation matrix of the state is characterized within a set of reasonable assumptions, and the strength of the entanglement is gauged using measures of the degree of inseparability and the degree of EPR paradox. We introduce controlled decoherence in the form of optical loss to the entangled state, and demonstrate qualitative differences in the response of the degrees of inseparability and EPR paradox to this loss. The entanglement is represented on a photon number diagram that provides an intuitive and physically relevant description of the state. We calculate efficacy contours for several quantum information protocols on this diagram, and use them to predict the effectiveness of our entanglement in those protocols.
Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for $d$-dimensional bipartite quantum systems, which are more powerful than the corresponding ones introduced in [C. Spengler, M. Huber, S. Brierley, T. Adaktylos, and B.C. Hiesmayr, Phys. Rev. A textbf{86}, 022311 (2012); B. Chen, T. Ma, and S.M. Fei, Phys. Rev. A textbf{89}, 064302 (2014); B. Chen, T. Li, and S.M. Fei, arXiv:1406.7820v1 [quant-ph] (2014)]. Some states such as Werner states and Bell-diagonal states are used to further illustrate the efficiency of the presented criteria.
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