Experimental Extraction of Secure Correlations from a Noisy Private State

We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The privacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies to extract the key is exposed by an implementation of an entanglement distillation protocol for the produced state.

Figure 1

Experimental setup. (a) Preparation of noisy private states. Two maximally entangled photon pairs are generated in two nonlinear crystals $XX$, collected from four directions $A{A}^{\prime }B{B}^{\prime }$ shown in the inset, and subjected to polarization transformations implemented with quarter wave plates (QWP) and half wave plates (HWP). $D$, Soleil-Babinet compensators; IF, interference filters; SMF, single-mode fibers. (b) Polarization analyzers. PBS, polarizing beam splitter; MMF, multimode fibers; APD, avalanche photodiodes.

Figure 2

Reconstructed private state. (a) Absolute values of density matrix elements in the ${\sigma }_y$ basis reconstructed using KF method. (b) Diagonal KF values [dark gray (orange), with error bars] compared with the ML results [light gray (yellow)].

Figure 3

Two-qubit $AB$ state. (a) Absolute values of the elements of the reduced density matrix obtained by tracing out qubits $A^{\prime }$ and $B^{\prime }$. (b),(c) Absolute values of the elements of density matrices conditioned upon finding qubits $A^{\prime }$ and $B^{\prime }$ in identical (b) or orthogonal (c) states when measured in the same basis.