Making use of the polarization of photons, we present a new method to realize quantum communication using any qubit through a mixture or pure state as an ancilla.
Tomography allows one to estimate the density matrix describing the state an ensemble of quantum systems are prepared in (for example, polarization tomography determines the polarization state of a beam of identically prepared photons). In general, it is not possible to uniquely decompose the density matrix into its pure state components. Agarwal et al. proposed a protocol which, for a mixture composed of any two pure states of a qubit (with arbitrary probabilities), allows an observer to infer not only the density matrix but the identity of those specific pure states and their weights - the additional requirement being that the qubits arrive in pairs, where both qubits in each pair are in the same state. We experimentally demonstrate this learning-from-pairs concept using photons in the polarization degree of freedom. We use tomography to measure a sequence of single photons and make use of their time-of-arrival information to 'pair up' the photons after the measurement. From here we are able to infer the photons' polarization states and their respective probabilities, and we demonstrate this for various different choices of polarization states and ratios. Finally, we investigate our ability to discriminate between two equal mixtures of distinct pairs of orthogonal polarization states. We find that on the order of approx. 10e4 photons is typically enough to achieve tomography fidelities of approximately 0.9999. This is sufficient to discriminate between two different preparations of the same mixed state, differing by angles of less than 5 degrees between the pure states used in the two preparations.
Quantum polarization is an important property that has been extensively used for quantum communication purposes. In this work, the mixture of an unpolarized two-mode state and a two-mode pure state is analysed. This mixture is controlled by a single parameter, namely the degree of purity. The quantum polarization of the two-mode mixed state is discussed using the quantum Stokes parameters and the quantum degree of polarization. A relation between the degree of purity and the quantum degree of polarization is established. The mixture is used to model coherent light amplified by an erbium-doped fibre amplifier, which focuses the loss of polarization due to the unpolarized light resulting from spontaneous emission. Finally, the use of such a mixed state in the quantum key distribution using multiphoton pulses is analysed.