An optical procedure in the context of continuous variables to verify bipartite entanglement without destroying both systems and their entanglement is proposed. To perform the nondestructive verification of entanglement, the method relies on beam-splitter and quantum nondemolition (QND) interactions of the signal modes with two ancillary probe modes. The probe modes are measured by homodyne detections, and the obtained information is used to feed forward modulation of signal modes, concluding the procedure. Characterizing the method by figures of merit used in QND processes, we can establish the conditions for an effectively quantum scheme. Based on such conditions, it is shown that the classical information acquired from the homodyne detections of probe modes is sufficient to verify the entanglement of the output signal modes. The processing impact due to added noise on the output entanglement is assessed in the case of Gaussian modes.
An optical procedure in the context of continuous variables to verify bipartite entanglement without destroying both systems and their entanglement is proposed. To perform the nondestructive verification of entanglement, the method relies on beam-splitter and quantum nondemolition (QND) interactions of the signal modes with two ancillary probe modes. The probe modes are measured by homodyne detections, and the obtained information is used to feed forward modulation of signal modes, concluding the procedure. Characterizing the method by figures of merit used in QND processes, we can establish the conditions for an effectively quantum scheme. Based on such conditions, it is shown that the classical information acquired from the homodyne detections of probe modes is sufficient to verify the entanglement of the output signal modes. The processing impact due to added noise on the output entanglement is assessed in the case of Gaussian modes.
The quantum nondemolition (QND) measurement is one of the most studied quantum measurement procedures. Usually, such a process involves the coupling of a single system of interest, called signal, with a single probe system, so that the relevant information in the signal system is indirectly measured by observing the probe system. Here we extend the concept of quantum nondemolition interaction to the cases in which the signal and the probe systems are each one multipartite continuous-variable system. Specifically, we propose a general scheme that performs the multipartite QND interactions, relying on beam-splitter couplings between the signal and probe modes with only two ancillary modes prepared offline in squeezed states. The scheme is also composed of homodyne detection and feedforward modulation. The ancillary modes are detected in the process, providing photocurrents for postmodulation of the output systems, as well as sufficient information to calculate genuine multipartite entanglement conditions of the input systems and to monitor similar conditions of the output systems.
Three different methods have been discussed to verify continuous variable entanglement of intense light beams. We demonstrate all three methods using the same setup to facilitate the comparison. The nonlinearity used to generate entanglement is the Kerr effect in optical fibers. Due to the brightness of the entangled pulses, standard homodyne detection is not an appropriate tool for the verification. However, we show that by using large asymmetric interferometers on each beam individually, two noncommuting variables can be accessed and the presence of entanglement verified via joint measurements on the two beams. Alternatively, we witness entanglement by combining the two beams on a beam splitter that yields certain linear combinations of quadrature amplitudes which suffice to prove the presence of entanglement.
Two Kerr-squeezed optical beams can be combined in a beam splitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient, and proven technology of homodyne detection may be used for their characterization. A physical demonstration maintaining the important features of the model could be realized using optical fibers, beam splitters, and homodyne detection.
The efficient witnessing and certification of entanglement is necessitated by its ubiquitous use in various aspects of quantum technologies. In the case of continuous-variable bipartite systems, the Shchukin-Vogel hierarchy gives necessary conditions for separability in terms of moments of the mode operators. In this work we derive mode-operator-based witnesses for continuous-variable bipartite entanglement relying on the interference of two states. Specifically, we show how one can access higher moments of the mode operators, crucial for detecting entanglement of non-Gaussian states, using a single beamsplitter with variable phase and photon-number-resolving detectors. We demonstrate that the use of an entangled state paired with a suitable reference state is sufficient to detect entanglement in, e.g., two-mode squeezed vacuum, NOON states, and mixed entangled cat states. We also take into account experimental noise, including photon loss and detection inefficiency, as well as finite measurement statistics.
Entangled photons are ideally suited to the transmission of photonic quantum information. Mitigating the effects of decoherence is fundamental to distributing photonic entanglement across large distances. One such proposal is entanglement distillation, in which operations on a large ensemble of weakly entangled states generate a smaller ensemble of more strongly entangled states. In this thesis, we experimentally and theoretically analyse various tools required for demonstrating continuous-variable (CV) entanglement distillation, following the proposal by Browne et al., [Phys. Rev. A 67, 062320 (2003)]. Specifically, we propose figures of merit to account for the practical limitations of non-deterministic non-Gaussian operations, and analyse the experimental parameters necessary to optimise them. We develop a source of pulsed two-mode squeezed states, which are the initial states of our entanglement distillation protocol. We use weak-field homodyne detection as a phase-dependent photon counting detector, and demonstrate its utility in conditional state generation. Using these states, we demonstrate sub-binomial light as a tool for benchmarking quantum states. Finally, we applied two-mode weak-field homodyne detection to two entangled states and demonstrate correlations in the photon counting statistics which depend on a joint phase from two independent local oscillators. This setup is sufficient to apply an entanglement witness developed by Puentes et al. [New J. Phys. 12, 033042 (2010)]. Despite encouraging simulations, we do not witness entanglement with this scheme, which we attribute to a noise source unaccounted for in the simulations. Although we do not demonstrate entanglement distillation outright, the tools we develop to do so represent a general, hybrid approach to CV quantum optics. Developing tools such as phase-resolved projective measurement on two-mode states allows us to probe both the wave and particle nature of entangled light at the single-photon level. Using and expanding these techniques to probe larger quantum systems may prove useful in studies of fundamental physics and quantum enhanced technologies.
We analyse the entanglement nature of quantum complementarity in individual and simultaneous continuous-variable (CV) quantum nondemolition measurements of coordinate and momentum. The complementarity expressed by the uncertainty relations is compared with an information-theoretical analysis of the quantum correlations. To demonstrate the entanglement nature, new CV quantum erasing experiments are suggested, employing only Gaussian states and feasible quantum optical devices, as parametrical processes, beamsplitters and homodyne detections.