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arXiv:1912.00067

Single-shot deterministic entanglement between non-interacting systems with linear optics

Leigh S. Martin, K. Birgitta Whaley

Published Nov 29, 2019• 7 citations
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Abstract

Measurement-based heralded entanglement schemes have served as the primary link between physically separated qubits in most quantum information platforms. However, the impossibility of performing a deterministic Bell measurement with linear optics bounds the success rate of the standard protocols to at most 50%, which means that the entanglement of the unheralded state is zero. Here we show that the ability to perform feedback during the measurement process enables unit success probability in a single shot. Our primary feedback protocol, based on photon counting retains the same robustness as the standard Barrett-Kok scheme, while doubling the success probability even in the presence of loss. In superconducting circuits, for which homodyne detectors are more readily available than photon counters, we give another protocol that can deterministically entangle remote qubits given existing parameters. In constructing the latter protocol, we derive a general expression for locally optimal control that applies to any continuous, measurement-based feedback problem.

DOI
10.48550/arxiv.1912.00067

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Measurement-based heralded entanglement schemes have served as the primary link between physically separated qubits in most quantum information platforms. However, the impossibility of performing a deterministic Bell measurement with linear optics bounds the success rate of the standard protocols to at most 50%, which means that the entanglement of the unheralded state is zero. Here we show that the ability to perform feedback during the measurement process enables unit success probability in a single shot. Our primary feedback protocol, based on photon counting retains the same robustness as the standard Barrett-Kok scheme, while doubling the success probability even in the presence of loss. In superconducting circuits, for which homodyne detectors are more readily available than photon counters, we give another protocol that can deterministically entangle remote qubits given existing parameters. In constructing the latter protocol, we derive a general expression for locally optimal control that applies to any continuous, measurement-based feedback problem.
We consider the task of deterministically entangling two remote qubits using joint measurement and feedback, but no directly entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can be modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Finally, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.
Remote entanglement of distant, noninteracting quantum entities is a key primitive for quantum information processing. We present a protocol to remotely entangle two stationary qubits by first entangling them with propagating ancilla qubits and then performing a joint two-qubit measurement on the ancillas. Subsequently, single-qubit measurements are performed on each of the ancillas. We describe two continuous variable implementations of the protocol using propagating microwave modes. The first implementation uses propagating $\mathrm{Schr}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{o}}$ dinger cat states as the flying ancilla qubits, a joint-photon-number-modulo-2 measurement of the propagating modes for the two-qubit measurement, and homodyne detections as the final single-qubit measurements. The presence of inefficiencies in realistic quantum systems limit the success rate of generating high fidelity Bell states. This motivates us to propose a second continuous variable implementation, where we use quantum error correction to suppress the decoherence due to photon loss to first order. To that end, we encode the ancilla qubits in superpositions of Schr\"odinger cat states of a given photon-number parity, use a joint-photon-number-modulo-4 measurement as the two-qubit measurement, and homodyne detections as the final single-qubit measurements. We demonstrate the resilience of our quantum-error-correcting remote entanglement scheme to imperfections. Further, we describe a modification of our error-correcting scheme by incorporating additional individual photon-number-modulo-2 measurements of the ancilla modes to improve the success rate of generating high-fidelity Bell states. Our protocols can be straightforwardly implemented in state-of-the-art superconducting circuit-QED systems.
The act of measuring optical emissions from two remote qubits can entangle them. By demanding that a photon from each qubit reaches the detectors, one can ensure that no photon was lost. But retaining both photons is rare when loss rates are high, as in Moehring et al. where 30 successes occurred per 10(9) attempts. We describe a means to exploit the low grade entanglement heralded by the detection of a lone photon: A subsequent perfect operation is quickly achieved by consuming this noisy resource. We require only two qubits per node, and can tolerate both path length variation and loss asymmetry. The impact of photon loss upon the failure rate is then linear; realistic high-loss devices can gain orders of magnitude in performance and thus support quantum computing.
We present a detailed analysis of the Bell measurement scheme proposed in Lee et al. [Phys. Rev. Lett. 114, 113603 (2015)] based on a logical qubit using Greenberger-Horne-Zeilinger entanglement of photons. The success probability of the proposed Bell measurement can be made arbitrarily high using only linear optics as the number of photons in a logical qubit increases. We compare our scheme with all the other proposals, using single-photon qubits, coherent-state qubits, or hybrid qubits, suggested to enhance the efficiency of the Bell measurement. As a remarkable advantage, our scheme requires only photon on-off measurements, while photon number resolving detectors are necessary for all the other proposals. We find that the scheme based on coherent-state qubits shows the best performance with respect to the attained success probability in terms of the average number of photons used in the process, while our scheme outperforms the schemes using single-photon qubits. We finally show that efficient quantum communication and fault-tolerant quantum computation can be realized using our approach.
Scaling quantum computation beyond the capacity of a single quantum processing unit requires quantum interconnects between modular processors. Optical photons are natural carriers for distributing entanglement between these processors. Most loss-resilient protocols use photonic Bell-state measurements based on the linear-optics type-II fusion gate. The resulting entanglement rate scales quadratically with each processor's typically low photon-delivery probability. Here we analyze a memory-assisted quantum interconnect using a near-deterministic, robust photon--atom controlled-ZZZ gate via a single atom trapped in a high-finesse cavity. Detecting and measuring a photon from one processor heralds entanglement between that processor and the atom. This entanglement is preserved while the process repeats with the second processor until the second photon is detected and measured. Reading out the atomic qubit finalizes the entanglement between the processors. As the entanglement is mediated by the atom, the photons from both processors do not need to be indistinguishable, removing a major source of infidelity. Furthermore, by removing the simultaneous photon-arrival requirement, the protocol allows the entanglement rate to scale linearly rather than quadratically with photon-arrival probability over a wide parameter range. We derive entanglement rates under realistic parameters, accounting for decay of the atom's entanglement with the first processor and for decoherence caused by unheralded photon interactions. The nanosecond-scale of the gate and read-out operations leads to orders-of-magnitude entanglement-rate gain over linear optics, removing a key bottleneck in modular quantum computing.
On-demand creation of entanglement between distant qubits is a necessary ingredient for distributed quantum computation. We propose an entanglement scheme that allows for single-shot deterministic entanglement creation by detecting a single photon passing through a Mach–Zehnder interferometer with one transmon qubit in each arm. The entanglement production essentially relies on the fact that superconducting microwave structures allow one to achieve strong coupling between the qubit and the photon. By detecting the photon via a photon counter, a parity measurement is implemented and the wave function of the two qubits is projected onto a maximally entangled state. Most importantly, the entanglement generation is heralded such that our protocol is not susceptible to photon loss due to the indivisible nature of single photons.