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Physical Review A

Characterizing entanglement in qubits created with spatially correlated twin photons

Leonardo Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, Sebastião Pádua

Published Sep 12, 2007• 66 citations
Publisher

Abstract

We characterize entanglement in two-qubit pure states encoded in transverse momenta of twin photons obtained from spontaneous parametric down-conversion. Two alternate methods are employed: (i) measurement of conditional interference patterns and (ii) measurement of the marginal probability that yields the single-photon interference pattern. Both methods are local with classical communication and rely on Schmidt decomposition of the quantum state, which is generated by letting the photons propagate through an appropriate lens system. In both cases we can obtain the concurrence either through the Schmidt coefficients in the first method or directly relating the concurrence to the visibility of the interference pattern in the second one.

DOI
10.1103/physreva.76.032314

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We characterize entanglement in two-qubit pure states encoded in transverse momenta of twin photons obtained from spontaneous parametric down-conversion. Two alternate methods are employed: (i) measurement of conditional interference patterns and (ii) measurement of the marginal probability that yields the single-photon interference pattern. Both methods are local with classical communication and rely on Schmidt decomposition of the quantum state, which is generated by letting the photons propagate through an appropriate lens system. In both cases we can obtain the concurrence either through the Schmidt coefficients in the first method or directly relating the concurrence to the visibility of the interference pattern in the second one.
We introduce and experimentally demonstrate a method to measure the Schmidt number of pure two-photon states entangled in transverse-mode structure. Our method is based on the connection between the Schmidt decomposition in quantum theory and the coherent-mode decomposition in classical coherence theory. We apply the method to two-photon states generated by spontaneous parametric down conversion and show that our results are in excellent agreement with numerical calculations based on the Schmidt decomposition.
The measurement of the correlation between two quantum systems or particles has a broad significance in physics and also plays a central role in the fields of quantum optics and quantum information science. We propose a method of measuring the correlation between the transverse momenta of two photons, in which one only needs to detect one of the photons. We show that it is possible to generate a single-photon fringe pattern by using two spatially separated identical biphoton sources. The fringes are similar to the ones observed in a Michelson interferometer and possess certain remarkable properties. A striking feature of the fringes is that although the pattern is obtained by detecting one photon only of each photon pair, the fringes shift due to a change in the optical path traversed by the undetected photon; the shift is characterized by a combination of wavelengths of both photons. Using this method one can, therefore, measure the wavelength of a photon without detecting it. The visibility of the fringes diminishes as the correlation between the transverse momenta of twin photons decreases: visibility is unity for maximum momentum correlation and zero for no momentum correlation. This dependence allows us to determine the momentum correlation between both photons from the visibility of the fringe pattern obtained by detecting one of the photons only. Our method can potentially be generalized to other quantum entities.
We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.
Using two parametric down-converters, it is possible to prepare twin photons in position-entangled states, where the photons are labelled by their birth position. We have measured the interference between the two probability amplitudes for a twin-photon pair: of being born in the first crystal or in the second one. The oscillation frequency of the coincidence pattern can be varied through independent phase differences in the signal and idler beams. Entangled states in position and also in the polarization sub-space can be prepared with this source. In this case, measurement of the position interference can give us information about the degree of polarization entanglement.
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.
We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric down-conversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional intensity measurements, is shown to be only able to characterize entanglement in the near and far field zones of the source. Therefore we also follow a different approach. By evaluating the first-order coherence of a subsystem of the state we can quantify its entanglement. Unlike previous measurements, which determine the Fedorov ratio via intensity correlations, our setup is sensitive to both phase and modulus of the biphoton state and thus always grants experimental access to the full transverse entanglement of the SPDC state. It is shown theoretically that this scheme represents a direct measurement of the Schmidt number.