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arXiv:2009.02829 · Physical Review A

Characterizing mixed-state entanglement through single-photon interference

Mayukh Lahiri, Radek Łapkiewicz, Armin Hochrainer, Gabriela Barreto Lemos, Anton Zeilinger

Published Jul 6, 2021• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.104.013704

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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.
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 realize a conceptually new method for verifying and measuring entanglement in a class of two-part (bipartite) mixed states. Contrary to the approaches known to date, in our experiment we verify and measure entanglement in mixed quantum bipartite states by detecting only one subsystem, the other remains undetected. Only one copy of the mixed or pure state is used but that state is in a superposition of having been created in two identical sources. We show that information shared in entangled systems can be accessed through single-particle interference patterns. Our experiment enables entanglement characterization even when one of the subsystems cannot be detected, for example, when suitable detectors are not available.
Conventional methods of measuring entanglement in a two-qubit photonic mixed state require detection of both qubits. We generalize a recently introduced method which does not require detection of both qubits, by extending it to cover a wider class of entangled states. Specifically, we present a detailed theory that shows how to measure entanglement in a family of two-qubit mixed states, obtained by generalizing Werner states, without detecting one of the qubits. Our method is interferometric and does not require any coincidence measurement or postselection. We also perform a quantitative analysis of anticipated experimental imperfections. We show that the method is resistant to a decrease in the interference visibility resulting from such imperfections.
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.
Single-photon sources are a fundamental resource in quantum optics and quantum information science. Photons with differing spectral and temporal shapes do not interfere well and inhibit the performance of quantum applications such as linear optics quantum computing, boson sampling, and quantum networks. Indistinguishability and purity of photons emitted from different sources are crucial properties for many quantum applications. The ability to determine the state of single-photon sources therefore provides a means to assess their quality, compare different sources, and provide feedback for source tuning. Here, we propose and demonstrate a single-configuration experimental method enabling complete characterization of the spectral-temporal state of a pulsed single-photon source having both pure and mixed states. The method involves interference of the unknown single-photon source with a reference at a balanced beam splitter followed by frequency-resolved coincidence detection at the outputs. Fourier analysis of the joint-spectral two-photon interference pattern reveals the density matrix of the single-photon source in the frequency basis. We present an experimental realization of this method for pure and mixed state pulsed single-photon sources.