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arXiv:1809.09264 · Physical Review A

Boosting linear-optical Bell measurement success probability with predetection squeezing and imperfect photon-number-resolving detectors

Thomas Kilmer, Saikat Guha

Published Mar 1, 2019• 20 citations
arXivHTMLPDF

Abstract

Linear-optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability ${p}_{s}$ no higher than 0.5. However, predetection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ${p}_{s}\ensuremath{\approx}0.643$. The ability to achieve ${p}_{s}>0.5$ has been found to be critical in resource-efficient realizations of linear-optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of ${p}_{s}>0.5$ is not known to be the maximum achievable using squeezing, thereby leaving it open whether close-to-$100%$ efficient BSM might be achievable using squeezing as a resource. In this paper, we report insights on why squeezing-enhanced BSM achieves ${p}_{s}>0.5$. Using this, we show that the previously reported ${p}_{s}\ensuremath{\approx}0.643$ at single-mode squeezing strength $r=0.6585$---for unambiguous state discrimination (USD) of all four Bell states---is an experimentally unachievable point result, which drops to ${p}_{s}\ensuremath{\approx}0.59$ with the slightest change in $r$. We, however, show that squeezing-induced boosting of ${p}_{s}$ with USD operation is still possible over a continuous range of $r$, with an experimentally achievable maximum occurring at $r=0.5774$, achieving ${p}_{s}\ensuremath{\approx}0.596$. Finally, deviating from USD operation, we explore a trade space between ${p}_{s}$, the probability with which the BSM circuit declares a ``success,'' versus the probability of error ${p}_{e}$, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some ${p}_{e}>0$, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with ${p}_{s}$ exceeding what is possible with traditionally studied USD operation of BSMs.

DOI
10.1103/physreva.99.032302

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Linear-optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability ps{p}_{s}ps​ no higher than 0.5. However, predetection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ps\ensuremath≈0.643{p}_{s}\ensuremath{\approx}0.643ps​\ensuremath≈0.643. The ability to achieve ps>0.5{p}_{s}>0.5ps​>0.5 has been found to be critical in resource-efficient realizations of linear-optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of ps>0.5{p}_{s}>0.5ps​>0.5 is not known to be the maximum achievable using squeezing, thereby leaving it open whether close-to-100100%100 efficient BSM might be achievable using squeezing as a resource. In this paper, we report insights on why squeezing-enhanced BSM achieves ps>0.5{p}_{s}>0.5ps​>0.5. Using this, we show that the previously reported ps\ensuremath≈0.643{p}_{s}\ensuremath{\approx}0.643ps​\ensuremath≈0.643 at single-mode squeezing strength r=0.6585r=0.6585r=0.6585---for unambiguous state discrimination (USD) of all four Bell states---is an experimentally unachievable point result, which drops to ps\ensuremath≈0.59{p}_{s}\ensuremath{\approx}0.59ps​\ensuremath≈0.59 with the slightest change in rrr. We, however, show that squeezing-induced boosting of ps{p}_{s}ps​ with USD operation is still possible over a continuous range of rrr, with an experimentally achievable maximum occurring at r=0.5774r=0.5774r=0.5774, achieving ps\ensuremath≈0.596{p}_{s}\ensuremath{\approx}0.596ps​\ensuremath≈0.596. Finally, deviating from USD operation, we explore a trade space between ps{p}_{s}ps​, the probability with which the BSM circuit declares a ``success,'' versus the probability of error pe{p}_{e}pe​, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some pe>0{p}_{e}>0pe​>0, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with ps{p}_{s}ps​ exceeding what is possible with traditionally studied USD operation of BSMs.
Abstract Fault-tolerant fusion-based photonic quantum computing (FBQC) greatly relies on entangling two-photon measurements, called fusions. These fusions can be realized using linear-optical projective Bell-state measurements (BSMs). These linear-optical BSMs are limited to a success probability of 50%, greatly reducing the performance of FBQC schemes. The performance of FBQC can be improved using boosting, thus achieving higher success probabilities by adding additional resources. Here, we realize a boosted BSM using a 4 × 4 multiport splitter and an additional entangled photon pair, allowing for a success probability of up to 75%. In our experiment, we obtain a success probability for our boosted BSM of (69.3 ± 0.3)%, clearly exceeding the 50% limit. We further demonstrate the significance of our boosted BSM for FBQC, showing a threefold increase in robustness to photon loss and a significant reduction of the logical error rates.
Bell-state projections serve as a fundamental basis for most quantum communication and computing protocols today. However, with current Bell-state measurement schemes based on linear optics, only two of four Bell states can be identified, which means that the maximum success probability of this vital step cannot exceed 50%50\%50%. Here, we experimentally demonstrate a scheme that amends the original measurement with additional modes in the form of ancillary photons, which leads to a more complex measurement pattern, and ultimately a higher success probability of 62.5%62.5\%62.5%. Experimentally, we achieve a success probability of (57.9±1.4)%(57.9 \pm 1.4)\%(57.9±1.4)%, a significant improvement over the conventional scheme. With the possibility of extending the protocol to a larger number of ancillary photons, our work paves the way towards more efficient realisations of quantum technologies based on Bell-state measurements.
Fault tolerance is essential for scalable quantum technologies and is enabled by quantum error-correction codes. Bell-state measurements (BSMs) are a fundamental building block for modern quantum technologies such as measurement-based quantum computation and fusion-based quantum computation, as well as quantum networks. Therefore, performing BSMs on error-corrected qubits is a necessary step for achieving fault tolerance in these applications. In this work, we realise a logical BSM using linear optics, based on a two-qubit repetition code, an instance of a quantum parity code that allows detection of bit-flip errors, and experimentally achieve a mean success probability of (70.8 +/- 0.4)%. While standard linear-optical BSMs are fundamentally limited to a maximum success probability of 50%, this increased success probability enables higher secure key rates in quantum communication and facilitates the generation of large graph states for quantum computation. Since fault-tolerant schemes require error-correction codes regardless, this improvement comes at no additional resource overhead. Our results demonstrate that error-correction codes can be used to surpass the linear-optics limit of BSMs, which is an important step towards practical, fault-tolerant, and scalable photonic quantum technologies.
Bell-state projections serve as a fundamental basis for most quantum communication and computing protocols today. However, with current Bell-state measurement schemes based on linear optics, only two of four Bell states can be identified, which means that the maximum success probability of this vital step cannot exceed 50%. Here, we experimentally demonstrate a scheme that amends the original measurement with additional modes in the form of ancillary photons, which leads to a more complex measurement pattern, and ultimately a higher success probability of 62.5%. Experimentally, we achieve a success probability of (57.9 ± 1.4)%, a substantial improvement over the conventional scheme. With the possibility of extending the protocol to a larger number of ancillary photons, our work paves the way toward more efficient realizations of quantum technologies based on Bell-state measurements.
Bell measurements, entailing the projection onto one of the Bell states, play a key role in quantum information and communication, where the outcome of a variety of protocols crucially depends on the success probability of such measurements. Although in the case of qubit systems, Bell measurements can be implemented using only linear optical components, the same result is no longer true for qudits, where at least the use of ancillary photons is required. In order to circumvent this limitation, one possibility is to introduce nonlinear effects. In this work, we adopt the latter approach and propose a scalable Bell measurement scheme for high-dimensional states, exploiting multiple squeezer devices applied to a linear optical circuit for discriminating the different Bell states. Our approach does not require ancillary photons, is not limited by the dimension of the quantum states, and is experimentally scalable, thus paving the way toward the realization of an effective high-dimensional Bell measurement.
Pairwise fusion gates are linear-optical measurements that herald Bell projections onto two-rail subspaces of two ddd-rail single-photon qudits. Without ancillary input photons, these passive measurements succeed with probability 1−d−11-d^{-1}1−d−1, with all failures confined to the diagonal logical subspace. We show that identical single-mode squeezers applied to the 2d2d2d interferometer outputs before photon-number-resolving detection recover part of this structured failure sector. Photon-number parity preserves the successful off-diagonal fusion signatures, while selected all-even patterns yield POVM elements proportional to definite pairwise Bell projectors. We derive the exact logical-space POVM and prove that a diagonal pattern is accepted if and only if its photon-number-imbalance vector has exactly two nonzero components of equal magnitude. The resulting closed elliptic-integral expression increases the ideal success probability, for instance, from 75%75\%75% to 79.62%79.62\%79.62% for d=4d=4d=4, and from 83.33%83.33\%83.33% to 87.15%87.15\%87.15% for d=6d=6d=6. With a representative finite detector saturation threshold, nsat=7n_{\rm sat}=7nsat​=7, the respective certified values remain 78.84%78.84\%78.84% and 86.71%86.71\%86.71%. These results establish active Gaussian processing as a method for recycling structured measurement failures without ancillary input photons, at the cost of 2d2d2d squeezing operations and a larger photon-number range at detection.