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arXiv:2105.06306 · Physical Review Research

Compact linear optical scheme for Bell state generation

Suren A. Fldzhyan, M. Yu. Saygin, S. P. Kulik

Published Oct 13, 2021• 20 citations
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Abstract

The capability of linear optics to generate entangled states is exploited in photonic quantum information processing, however, it is challenging to obtain entangled logical qubit states. We report, to the best of our knowledge, the most compact scheme producing the dual-rail-encoded Bell states out of four single photons. Our scheme requires a five-mode interferometer and a single photon detector, while the previously known schemes use six-mode interferometers and two photon detectors. Using computer optimization, we have found a decomposition of the five-mode interferometer with a minimum number of beam splitters and phase-shift elements. Besides compactness, our scheme also offers a success probability of $1/9$, which is higher than $2/27$ provided by the six-mode counterparts. The analysis suggests that the elevated success probability is connected to a higher order of photon interference realized by our scheme, in particular, four-photon interference is implemented in our scheme, while three-photon interference was implemented in previous counterparts.

DOI
10.1103/physrevresearch.3.043031

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The capability of linear optics to generate entangled states is exploited in photonic quantum information processing, however, it is challenging to obtain entangled logical qubit states. We report, to the best of our knowledge, the most compact scheme producing the dual-rail-encoded Bell states out of four single photons. Our scheme requires a five-mode interferometer and a single photon detector, while the previously known schemes use six-mode interferometers and two photon detectors. Using computer optimization, we have found a decomposition of the five-mode interferometer with a minimum number of beam splitters and phase-shift elements. Besides compactness, our scheme also offers a success probability of 1/91/91/9, which is higher than 2/272/272/27 provided by the six-mode counterparts. The analysis suggests that the elevated success probability is connected to a higher order of photon interference realized by our scheme, in particular, four-photon interference is implemented in our scheme, while three-photon interference was implemented in previous counterparts.
Using only linear optical elements, the creation of dual-rail photonic entangled states is inherently probabilistic. Known entanglement generation schemes have low success probabilities, requiring large-scale multiplexing to achieve near-deterministic operation of quantum information processing protocols. In this paper, we introduce multiple techniques and methods to generate photonic entangled states with high probability, which have the potential to reduce the footprint of Linear Optical Quantum Computing (LOQC) architectures drastically. Most notably, we are showing how to improve Bell state preparation from four single photons to up to p=2/3, boost Type-I fusion to 75% with a dual-rail Bell state ancilla and improve Type-II fusion beyond the limits of Bell state discrimination.
We investigated the heralded generation of two-qubit dual-rail-encoded states by programmable linear optics. Two types of scheme generating the states from four single photons, which is the minimum possible to accomplish the task, were considered. The schemes have different detection patterns heralding successful generation events; namely, one-mode heralding, in which the two auxiliary photons are detected in one mode, and two-mode heralding, in which single photons are detected in each of the two modes simultaneously. We show that the dependencies of the schemes' success probabilities on the target state's degree of entanglement are essentially different. In particular, one-mode heralding yields greater efficiency for highly entangled states if the programmable interferometers can explore the full space of the unitary transfer matrices. The reverse is the case for weakly entangled states, where two-mode heralding is better. We found a minimal decomposition of the scheme with two-mode heralding that is programmed by one variable phase shift. We infer that the linear optical schemes designed specifically for the generation of two-qubit states are more efficient than schemes implementing known linear optical gate--based circuits. Our results reveal a substantial reduction of physical resources needed to generate some types of nonmaximally entangled multiqubit states used in quantum computing.
We present a semianalytical methodology to construct optimal linear-optical circuits for the heralded production of three-photon Greenberger-Horne-Zeilinger (3-GHZ) and two-photon Bell states. We provide a detailed description and analysis of the resulting optical schemes, which deliver success probabilities of 1/54 and 2/27 for dual-rail encoded 3-GHZ and Bell-state generation, respectively. Our results improve the known constructive bounds on the success probabilities for 3-GHZ states and are of particular importance for a ballistic quantum computing model [M. Gimeno-Segovia et al., Phys. Rev. Lett. 115, 020502 (2015)], for which these states provide an essential resource.
An important aspect of many linear optical quantum computing architectures is probabilistically generating small dual-rail qubit entangled states, or seed states. While many schemes to achieve this have been discovered, attention has been primarily focused on minimizing input resources and maximizing success probability rather than establishing a detailed understanding of linear-optical error performance. In this work, we develop a framework for resolving sensitivities to physically distinct errors in linear optical state generation, allowing us to identify precise ways in which these errors affect the properties of the output state. We use this framework to identify seed state generators in which destructive many-photon interference prevents detector loss and detector noise from causing a falsely successful heralding event. We show that this effect suppresses errors, for example cutting the effective loss on the output of particular Bell state generators in half relative to a standard scheme. We also present a new Bell state generator in which both detector loss and detector noise do not affect the quality of the output Bell state to first order, and a 4GHZ generator with >75% higher success probability than a standard circuit. In addition we provide some useful identities, bounds and invariants for studying linear optical seed state generation.
Probabilistic and destructive Bell-measurements, also known as fusions, constitute a fundamental primitive for photonic quantum technologies. These operations rely only on pairwise photonic interference, whereas the computational power of photonic quantum systems originates from many-body interference. Here, we introduce a family of high-efficiency linear-optical GHZ measurements based on four-mode interferometers and show that incorporating many-body interference into this ubiquitous primitive leads to more efficient entangling operations. For the four-photon case, the success probability is 9/329/329/32, and adaptive variants ensure that unsuccessful events project onto useful stabilizer states. We further show that the approach naturally generalizes to larger GHZ measurements, yielding an exponentially higher success probability than previous linear-optical schemes. Finally, we demonstrate practical advantages for graph-state resource generation, entanglement distribution between remote spin-photon interfaces, and fusion-based quantum computing. Our results establish high-efficiency many-body measurements as a new primitive for scalable photonic quantum information processing.
The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities above 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware.