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Register a new userProcessing multi-photon state through operation on single photon: methods and applications
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Multi-photon states are widely applied in quantum information technology. By the methods presented in this paper, the structure of a multi-photon state in the form of multiple single photon qubit product can be mapped to a single photon qudit, which could also be in separable product with other photons. This makes the possible manipulation of such multi-photon states in the way of processing single photon states. The optical realization of unknown qubit discrimination [B. He, J. A. Bergou, and Y.-H. Ren, Phys. Rev. A 76, 032301 (2007)] is simplified with the transformation methods. Another application is the construction of quantum logic gates, where the inverse transformations back to the input state spaces are also necessary. We especially show that the modified setups to implement the transformations can realize the deterministic multi-control gates (including Toffoli gate) operating directly on the products of single photon qubits.
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Entanglement verification and measurement is essential for experimental tests of quantum mechanics and also for quantum communication and information science. Standard methods of verifying entanglement in a bipartite mixed state require detection of both particles and involve coincidence measurement. We present a method that enables us to verify and measure entanglement in a two-photon mixed state without detecting one of the photons, i.e., without performing any coincidence measurement or postselection. We consider two identical sources, each of which can generate the same two-photon mixed state but they never emit simultaneously. We show that one can produce a set of single-photon interference patterns, which contain information about entanglement in the two-photon mixed state. We prove that it is possible to retrieve the information about entanglement from the visibility of the interference patterns. Our method reveals a distinct avenue for verifying and measuring entanglement in mixed states.
Entanglement is a fundamental feature of quantum mechanics, considered a key resource in quantum information processing. Measuring entanglement is an essential step in a wide range of applied and foundational quantum experiments. When a two-particle quantum state is not pure, standard methods to measure the entanglement require detection of both particles. We introduce a method in which detection of only one of the particles is required to characterize the entanglement of a two-particle mixed state. Our method is based on the principle of quantum interference. We use two identical sources of a two-photon mixed state and generate a set of single-photon interference patterns. The entanglement of the two-photon quantum state is characterized by the visibility of the interference patterns. Our experiment thus opens up a distinct avenue for verifying and measuring entanglement, and can allow for mixed state entanglement characterization even when one particle in the pair cannot be detected.
This thesis reports advances in the theory of design, characterization and simulation of multi-photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. This procedure effects an arbitrary $n_{s}n_{p}times n_{s}n_{p}$ unitary matrix on the state of light in $n_{s}$ spatial and $n_{p}$ internal modes. I devise an accurate and precise procedure for characterizing any multi-port linear optical interferometer using one- and two-photon interference. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision are attained by fitting experimental coincidence data to a curve simulated using measured source spectra. The efficacy of our characterization procedure is verified by numerical simulations. I develop group-theoretic methods for the analysis and simulation of linear interferometers. I devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU$(n)$ basis states, which reduce the canonical subgroup chain, for arbitrary $n$. The boson realizations are employed to construct $mathcal{D}$-functions, which are the matrix elements of arbitrary irreducible representations, of SU$(n)$ in the canonical basis. I show that immanants of principal submatrices of a unitary matrix $T$ are a sum of the diagonal $mathcal{D}(Omega)$-functions of group element $Omega$ over $t$ determined by the choice of submatrix and over the irrep $(lambda)$ determined by the immanant under consideration. The algorithm for $mathrm{SU}(n)$ $mathcal{D}$-function computation and the results connecting these functions with immanants open the possibility of group-theoretic analysis and simulation of linear optics.
Heralded single photons are prepared at a rate of ~100 kHz via conditional measurements on polarization-nondegenerate biphotons produced in a periodically poled KTP crystal. The single-photon Fock state is characterized using high frequency pulsed optical homodyne tomography with a fidelity of (57.6 +- 0.1)%. The state preparation and detection rates allowed us to perform on-the-fly alignment of the apparatus based on real-time analysis of the quadrature measurement statistics.
A strong limitation of linear optical quantum computing is the probabilistic operation of two-quantum bit gates based on the coalescence of indistinguishable photons. A route to deterministic operation is to exploit the single-photon nonlinearity of an atomic transition. Through engineering of the atom-photon interaction, phase shifters, photon filters and photon- photon gates have been demonstrated with natural atoms. Proofs of concept have been reported with semiconductor quantum dots, yet limited by inefficient atom-photon interfaces and dephasing. Here we report on a highly efficient single-photon filter based on a large optical non-linearity at the single photon level, in a near-optimal quantum-dot cavity interface. When probed with coherent light wavepackets, the device shows a record nonlinearity threshold around $0.3 pm 0.1$ incident photons. We demonstrate that directly reflected pulses consist of 80% single-photon Fock state and that the two- and three-photon components are strongly suppressed compared to the single-photon one.
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