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arXiv:2110.05309 · Physical Review A

Long-time Bell states of waveguide-mediated qubits via continuous measurement

Huiping Zhan, Huatang Tan

Published Mar 29, 2022• 5 citations
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Abstract

In this paper we consider a scheme for achieving long-time sustainable Bell states of two distant qubits mediated by a one-dimensional waveguide whose outputs are subjected to time-continuous photon counting or homodyne detection. In both of the detection cases, it is shown that different Bell states can be obtained, for different initial states, in the long-time regime. In particular, we find that, in the case of photon counting, a cyclic jump among Bell states can be formed once the first photon is registered. While in the homodyne-detection case we further reveal that any steady Bell state can be achieved independent of detection efficiency, with a probability of 50% . The underlying physical reason for this is also analyzed. Our scheme is advantageous over previous studies in which only transient or intermittent Bell states can be generated. The long-time Bell states of distant qubits can be used for constructing quantum networks.

DOI
10.1103/physreva.105.033715

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In this paper we consider a scheme for achieving long-time sustainable Bell states of two distant qubits mediated by a one-dimensional waveguide whose outputs are subjected to time-continuous photon counting or homodyne detection. In both of the detection cases, it is shown that different Bell states can be obtained, for different initial states, in the long-time regime. In particular, we find that, in the case of photon counting, a cyclic jump among Bell states can be formed once the first photon is registered. While in the homodyne-detection case we further reveal that any steady Bell state can be achieved independent of detection efficiency, with a probability of 50% . The underlying physical reason for this is also analyzed. Our scheme is advantageous over previous studies in which only transient or intermittent Bell states can be generated. The long-time Bell states of distant qubits can be used for constructing quantum networks.
Maximally entangled two-qubit states (Bell states) are of central importance in quantum technologies. We show that heralded generation of a maximally entangled state of two intrinsically open qubits can be realized in a one-dimensional (1D) system through strong coherent driving and continuous monitoring. In contrast to the natural idea that dissipation leads to decoherence and so destroys quantum effects, continuous measurement and strong interference in our 1D system generate a pure state with perfect quantum correlation between the two open qubits. Though the steady state is a trivial product state that has zero coherence or concurrence, we show that, with carefully tuned parameters, a Bell state can be generated in the system's quantum jump trajectories, heralded by a reflected photon. Surprisingly, this maximally entangled state survives the strong coherent state input-a classical state that overwhelms the system. This simple method to generate maximally entangled states using classical coherent light and photon detection may, since our qubits are in a 1D continuum, find application as a building block of quantum networks.
We discuss recent developments in measurement protocols that generate quantum entanglement between two remote qubits, focusing on the theory of joint continuous detection of their spontaneous emission. We consider a device geometry similar to that used in well-known Bell state measurements, which we analyze using a conceptually transparent model of stochastic quantum trajectories; we use this to review photodetection, the most straightforward case, and then generalize to the diffusive trajectories from homodyne and heterodyne detection as well. Such quadrature measurement schemes are a realistic two-qubit extension of existing circuit QED experiments, which obtain quantum trajectories by homodyning or heterodyning a superconducting qubit’s spontaneous emission, or an adaptation of existing optical measurement schemes to obtain jump trajectories from emitters. We mention key results, presented from within a single theoretical framework, and draw connections to concepts in the wider literature on entanglement generation by measurement (such as path information erasure and entanglement swapping). The photon which-path information acquisition, and therefore the two-qubit entanglement yield, is tunable under the homodyne detection scheme we discuss, at best generating equivalent average entanglement dynamics as in the comparable photodetection case. In addition to deriving this known equivalence, we extend past analyses in our characterization of the measurement dynamics: we include derivations of bounds on the fastest possible evolution toward a Bell state under joint homodyne measurement dynamics and characterize the maximal entanglement yield possible using inefficient (lossy) measurements.
We show how to generate Bell states and NNN-partite WWW states of long-distance superconducting (SC) qubits in a SC waveguide QED system, where SC qubits are coupled to an open microwave transmission line. In the two-qubit case, the Bell state of two long-distance qubits can be a dark state of the system by choosing appropriate system parameters. If one proper microwave pulse drives one of two qubits, the two qubits will evolve from their ground states to a Bell state. Further, we extend this scheme to the multiqubit case. We show that WWW states of NNN long-distance qubits can also be generated. Because both the Bell and WWW states are decoupled from the waveguide (i.e., dark states of the system), they are steady and have very long lifetimes in the ideal case without decoherence of qubits. In contrast to the ideal case, the presence of decoherence of qubits limits the lifetimes of the Bell and WWW states. Our study provides an alternative scheme for generating Bell states and NNN-partite WWW states in SC waveguide QED, which can be used to entangle long-distance nodes in waveguide quantum networks.
Maximally entangled two-qubit states (Bell states) are of central importance in quantum technologies. We show that heralded generation of a maximally entangled state of two intrinsically open qubits can be realized in a one-dimensional (1d) system through strong coherent driving and continuous monitoring. In contrast to the natural idea that dissipation leads to decoherence and so destroys quantum effects, continuous measurement and strong interference in our 1d system generate a pure state with perfect quantum correlation between the two open qubits. Though the steady state is a trivial product state which has zero coherence or concurrence, we show that, with carefully tuned parameters, a Bell state can be generated in the system's quantum jump trajectories, heralded by a reflected photon. Surprisingly, this maximally entangled state survives the strong coherent state input---a classical state that overwhelms the system. This simple method to generate maximally entangled states using classical coherent light and photon detection may, since our qubits are in a 1d continuum, find application as a building block of quantum networks.
We consider protocols to generate quantum entanglement between two remote qubits, through joint time-continuous detection of their spontaneous emission. We demonstrate that schemes based on homodyne detection, leading to diffusive quantum trajectories, lead to identical average entanglement yield as comparable photodetection strategies; this is despite substantial differences in the two-qubit state dynamics between these schemes, which we explore in detail. The ability to use different measurements to achieve the same ends may be of practical significance; the less-well-known diffusive scheme appears far more feasible on superconducting qubit platforms in the near term.
Establishing quantum entanglement between pairs of distant quantum memories (QMs) is essential for numerous applications in quantum networks. In this paper, we propose some heralded schemes for entanglement generation between multiple pairs of QMs placed in long-distance separated nodes, where the qubits are encoded on QMs coupled to a one-dimensional waveguide. By distributing a pair of spatial-polarization hyperentangled photons to two distant nodes, where each photon scatters with QMs, we can generate entanglement between multiple pairs of distant QMs. In our schemes, the faulty scattering events can be filtered out and discarded via detecting the polarization states of scattered photon components within each module QM. Moreover, the responses from single-photon detectors placed at the end of each node enable us to obtain direct entangled states between QMs in a heralded manner. Eventually, we theoretically extend the proposed schemes by demonstrating specific regularities that arise when entangling more pairs of QMs. With recent advancements in hyperentanglement generation, our schemes become increasingly feasible for practical implementation.