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arXiv:quant-ph/0303113 · IEEE Journal of Selected Topics in Quantum Electronics

Heralded two-photon entanglement from probabilistic quantum logic operations on multiple parametric down-conversion sources

T. B. Pittman, Michelle M. Donegan, Michael J. Fitch, B. C. Jacobs, J. D. Franson, Pieter Kok, Hwang Lee, Jonathan P. Dowling

Published Nov 1, 2003• 26 citations
arXivHTMLPDF

Abstract

An ideal controlled-NOT gate followed by projective measurements can be used to identify specific Bell states of its two input qubits. When the input qubits are each members of independent Bell states, these projective measurements can be used to swap the post-selected entanglement onto the remaining two qubits. Here we apply this strategy to produce heralded two-photon polarization entanglement using Bell states that originate from independent parametric down-conversion sources, and a particular probabilistic controlled-NOT gate that is constructed from linear optical elements. The resulting implementation is closely related to an earlier proposal by Sliwa and Banaszek, and can be intuitively understood in terms of familiar quantum information protocols. The possibility of producing a "pseudo-demand" source of two-photon entanglement by storing and releasing these heralded pairs from independent cyclical quantum memory devices is also discussed.

DOI
10.1109/jstqe.2003.820916

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An ideal controlled-NOT gate followed by projective measurements can be used to identify specific Bell states of its two input qubits. When the input qubits are each members of independent Bell states, these projective measurements can be used to swap the post-selected entanglement onto the remaining two qubits. Here we apply this strategy to produce heralded two-photon polarization entanglement using Bell states that originate from independent parametric down-conversion sources, and a particular probabilistic controlled-NOT gate that is constructed from linear optical elements. The resulting implementation is closely related to an earlier proposal by Sliwa and Banaszek, and can be intuitively understood in terms of familiar quantum information protocols. The possibility of producing a "pseudo-demand" source of two-photon entanglement by storing and releasing these heralded pairs from independent cyclical quantum memory devices is also discussed.
Heralded entangling quantum gates are an essential element for the implementation of large-scale optical quantum computation. Yet, the experimental demonstration of genuine heralded entangling gates with free-flying output photons in linear optical system, was hindered by the intrinsically probabilistic source and double-pair emission in parametric down-conversion. Here, by using an on-demand single-photon source based on a semiconductor quantum dot embedded in a micropillar cavity, we demonstrate a heralded controlled-NOT (CNOT) operation between two single photons for the first time. To characterize the performance of the CNOT gate, we estimate its average quantum gate fidelity of (87.8±1.2)%. As an application, we generated event-ready Bell states with a fidelity of (83.4±2.4)%. Our results are an important step towards the development of photon-photon quantum logic gates.
A double-heralding technique is presented for producing heralded entangled photon pairs from spontaneous parametric down-conversion (SPDC). Compared to the swap-heralded schemes studied in previous cascaded SPDC and zero-added-loss multiplexing (ZALM) proposals, this double-heralding technique is found to yield the most resource-efficient implementation in terms of minimizing the total number of sources and detectors required to achieve a specified rate and fidelity. This is achieved by reducing the number of modes and mode-sorting optics needed on the heralding path. Specifically, by immediately detecting any two signal photons from an array of down-converters, the corresponding idler photons can be projected onto an anti-correlated pair state which is shown to be unitarily equivalent to the state produced by swap-heralded sources, and hence can be used directly for long-range entanglement distribution in a ZALM architecture. Quasi-deterministic operation through two distinct multiplexing techniques is analyzed. The analysis derives expressions for the heralded pair probability and fidelity assuming realistic detectors with losses, dark counts, and partial photon number resolution (PNR), providing a framework for implementation of the source on a photonic integrated circuit (PIC).
We propose a scheme for building a heralded two-qutrit entangled state from polarized photons. An optical circuit is presented to build the maximally entangled two-qutrit state from two heralded Bell pairs and ideal threshold detectors. Several schemes are discussed for constructing the two Bell pairs. We also show how one can produce an unbalanced two-qutrit state that could be of general purpose use in some protocols. In terms of the applications of the maximally entangled qutrit state, we mainly focus on how to use the state to demonstrate a violation of the Collins–Gisin–Linden–Massar–Popescu inequality under the restriction of measurements which can be performed using linear optical elements and photon counting. Other possible applications of the state, such as for higher dimensional quantum cryptography, teleportation and generation of heralded two-qudit states, are also briefly discussed.
Distributing entangled states over potentially long distances provides a key resource for many protocols in quantum communication and quantum cryptography. Ideally, this should be implemented in a heralded manner. Starting with four single-photon states, we cascade two single-photon path-entangled states, coded in orthogonal polarizations, to distribute and herald polarization entanglement in a single quantum repeater link architecture. By tuning the input states to minimize (local) losses, the theoretically achievable fidelity to the target state without postselection approaches 1, while sacrificing heralding rates. We achieve a fidelity to the target state of over 95% after postselection, providing a benchmark for the experimental control and allowing a first demonstration of a device-independent quantum key distribution architecture capable of operation over relevant distances. We show that the fidelity of the heralded state without postselection scales predictably and also identify various practical challenges and error sources specific to this architecture, and model their effects on the generated state. While our experiment uses probabilistic photon-pair sources based on spontaneous parametric downconversion, many of these problems are also relevant for variants employing deterministic photon sources.
We propose probabilistic controlled-NOT and controlled-phase gates for qubits stored in the polarization of photons. The gates are composed of linear optics and photon detectors, and consume polarization entangled photon pairs. The fraction of the successful operation is only limited by the efficiency of the Bell-state measurement. The gates work correctly under the use of imperfect detectors and lossy transmission of photons. Combined with single-qubit gates, they can be used for producing arbitrary polarization states and for designing various quantum measurements.