Using the measured density matrix of a four photon GHZ state, created in our unique inductive setup, we calculated the density matrices of possible states with higher photon numbers and their entanglement and non-locality violation.
The generation of quantum entangled states of many particles is a central goal of quantum information science. Characterizing such states is a complex task that demands exponentially large resources as particles are being added. Previously, we demonstrated a resource efficient source that can generate, in principal, entanglement between any number of photons. This source recursively fuse photon pairs generated by a pulsed laser into a multiphoton entangled state. In the current work, we perform quantum state tomography on the photon pair source and quantum process tomography on the fusion operation. As a result, the full quantum Greenberger-Horne-Zeilinger (GHZ) state of any number of photons can be calculated. We explore the prospects of our scheme and calculate nonlocality and genuine \textit{N}-photon entanglement thresholds for states with up to twelve photons.
We have performed quantum-state tomography on several different single-photon entangled states, that is, states in which a single photon is shared between two possible paths. We begin by doing a tomographic reconstruction of density matrices in the subspace where a single photon is shared by two spatial modes. In this subspace we are able to create high-fidelity, path-entangled states. Also within this subspace we use the Akaike information criterion and Monte Carlo simulations to help us estimate the amount and source of state drift in our system. We find that the primary state drift is due to phase drifts and fluctuations on the order of $\ensuremath{\pi}/400$ in our experimental apparatus. We then use the single-photon subspace density matrices and further measurements to estimate density matrices in the larger space consisting of two modes containing up to one photon each. In this larger space we find that the concurrence of the density matrices is $C\ensuremath{\cong}0.08$ and is greater than 0 by at least 45 standard deviations, indicating that our states are indeed entangled.
Abstract Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.