Long-Range Coherence and Multiple Steady States in a Lossy Qubit Array

Abstract

We show that a simple experimental setting of a locally pumped and lossy array of two-level quantum systems can stabilize states with strong long-range coherence. Indeed, by explicit analytic construction, we show there is an extensive set of steady-state density operators, from minimally to maximally entangled, despite this being an interacting open many-body problem. Such nonequilibrium steady states arise from a hidden symmetry that stabilizes Bell pairs over arbitrarily long distances, with unique experimental signatures. We demonstrate a protocol by which one can selectively prepare these states using dissipation. Our findings are accessible in present-day experiments.

Generating Symmetry-Protected Long-Range Entanglement in Many-Body Systems

“…Entanglement between spatially distant qubits is perhaps the most counterintuitive and vital resource for distributed quantum computing [1,2]. However, despite a few special cases [3][4][5][6][7], there is no known general procedure to maximally entangle two distant parts of an interacting many-body system. Here we present a symmetry-based approach, whereby one applies several timed pulses to drive a system to a particular symmetry sector with maximal bipartite long-range entanglement.…”

“…These states possess a high persistency of entanglement [26] and can be used to efficiently distribute entanglement in a quantum network [3]. Unlike other protocols for creating rainbowlike states, we do not require the spin-spin interactions to be selectively switched off [14], individually fine tuned [3,4,22,24], or coupled with engineered dissipation for slow relaxation [5,6]. Instead, our scheme uses only local π pulses that are standard in experiments.…”

“…In particular, as shown in Ref. [6], there is a crucial symmetry relating to the entanglement between left and right halves of the chain, given by the symmetry operator Here, σz 0 measures the fermion-number parity at the center site, and the terms f † i f−i exchange spins between mirror-conjugate sites i and −i with a phase given by the total parity in between. The nature of this exchange becomes clearer if one rewrites Eq.…”

“…2), i.e., the number of generated Bell pairs grows linearly with the number of qubits, as does the preparation time t ∼ 2l/J. This scaling is on par with more complex protocols using two-qubit gates [14] or nonuniform coupling [3,4], and much faster than using correlated dissipation [5,6]. The fidelity can be enhanced further by optimal pulse shaping [30,31].…”

“…If a perturbation commutes with both Ĉ and σz 0 , the full time evolution of Ĉ is unaltered, as in the case of a uniform magnetic field along z. For other symmetrypreserving perturbations, including reflection-symmetric potentials [6] and dephasing at the center site, the fidelity may be affected but the generated entanglement is stable. If the symmetry itself is broken, Ĉ attains a maximum value during the protocol.…”