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We compare three different notions of concurrence to measure the polarizationentanglement of two-photon states generated by the biexciton cascade in aquantum dot embedded in a microcavity. We focus on the often-discussedsituation of a dot with finite biexciton binding energy in a cavity tuned tothe two-photon resonance. Apart from the time-dependent concurrence, which canbe assigned to the two-photon density matrix at any point in time, we studysingle- and double-time integrated concurrences commonly used in the literaturethat are based on different quantum state reconstruction schemes. We argue thatthe single-time integrated concurrence can be thought of as the concurrence ofphotons simultaneously emitted from the cavity without resolving the commonemission time, while the more widely studied double-time integrated concurrencerefers to photons that are neither filtered with respect to the emission timeof the first photon nor with respect to the delay time between the two emittedphotons. Analytic and numerical calculations reveal that the single-timeintegrated concurrence indeed agrees well with the typical value of thetime-dependent concurrence at long times, even in the presence of phonons.Thus, the more easily measurable single-time integrated concurrence givesaccess to the physical information represented by the time-dependentconcurrence. However, the double-time integrated concurrence shows a differentbehavior with respect to changes in the exciton fine structure splitting andeven displays a completely different trend when the ratio between the cavityloss rate and the fine structure splitting is varied while keeping theirproduct constant. This implies the non-equivalence of the physical informationcontained in the time-dependent and single-time integrated concurrence on theone hand and the double-time integrated concurrence on the other hand.

Comparison of different concurrences characterizing photon-pairs generated in the biexciton cascade in quantum dots coupled to microcavities