We compare three different notions of concurrence to measure the polarization entanglement of two-photon states generated by the biexciton cascade in a quantum dot embedded in a microcavity. The focus of the paper lies on the often-discussed situation of a dot with finite biexciton binding energy in a cavity tuned to the two-photon resonance. Apart from the time-dependent concurrence, which can be assigned to the two-photon density matrix at any point in time, we study single-and double-time integrated concurrences commonly used in the literature that are based on different quantum state reconstruction schemes. In terms of the photons detected in coincidence measurements, we argue that the single-time integrated concurrence can be thought of as the concurrence of photons simultaneously emitted from the cavity without resolving the common emission time, while the more widely studied double-time integrated concurrence refers to photons that are neither filtered with respect to the emission time of the first photon nor with respect to the delay time between the two emitted photons. Analytic and numerical calculations reveal that the single-time integrated concurrence indeed agrees well with the typical value of the time-dependent concurrence at long times, even when the interaction between the quantum dot and longitudinal acoustic phonons is accounted for. Thus, the more easily measurable single-time integrated concurrence gives access to the physical information represented by the time-dependent concurrence. However, the doubletime integrated concurrence shows a different behavior with respect to changes in the exciton fine structure splitting and even displays a completely different trend when the ratio between the cavity loss rate and the fine structure splitting is varied while keeping their product constant. This implies the non-equivalence of the physical information contained in the time-dependent and single-time integrated concurrence on the one hand and the double-time integrated concurrence on the other hand.arXiv:1712.02584v3 [cond-mat.mes-hall] 9 May 2018
We investigate the degree of entanglement quantified by the concurrence of photon pairs that are simultaneously emitted in the biexciton-exciton cascade from a quantum dot in a cavity. Four dot-cavity configurations are compared that differ with respect to the detuning between the cavity modes and the quantum dot transitions, corresponding to different relative weights of direct twophoton and sequential single-photon processes. The dependence of the entanglement on the exciton fine-structure splitting δ is found to be significantly different for each of the four configurations. For a finite splitting and low temperatures, the highest entanglement is found when the cavity modes are in resonance with the two-photon transition between the biexciton and the ground state and, in addition, the biexciton has a finite binding energy of a few meV. However, this widely used configuration is rather strongly affected by phonons such that other dot-cavity configurations, that are commonly regarded as less suited for obtaining high degrees of entanglement, become more favorable already at temperatures on the order of 10 K and above. If the cavity modes are kept in resonance with one of the exciton-to-ground-state transitions and the biexciton binding energy is finite, the entanglement drastically drops for positive δ with rising temperatures when T is below 4 K, but is virtually independent of the temperature for higher T .arXiv:1902.01683v2 [cond-mat.mes-hall]
Quantum cryptography harnesses quantum light, in particular single photons, to provide security guarantees that cannot be reached by classical means. For each cryptographic task, the security feature of interest is directly related to the photons’ non-classical properties. Quantum dot-based single-photon sources are remarkable candidates, as they can in principle emit deterministically, with high brightness and low multiphoton contribution. Here, we show that these sources provide additional security benefits, thanks to the tunability of coherence in the emitted photon-number states. We identify the optimal optical pumping scheme for the main quantum-cryptographic primitives, and benchmark their performance with respect to Poisson-distributed sources such as attenuated laser states and down-conversion sources. In particular, we elaborate on the advantage of using phonon-assisted and two-photon excitation rather than resonant excitation for quantum key distribution and other primitives. The presented results will guide future developments in solid-state and quantum information science for photon sources that are tailored to quantum communication tasks.
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