Creating long-range entangled Majorana pairs: from spin-1/2 twisted Kitaev to generalized XY chains

summary

The gist

The gist The maximally entangled rainbow-like Majorana pairing state can be reached, with a sequence of pairing pulses applied on the central unit cell of the system.

In short

The research investigates creating long-range entangled Majorana fermions in spin-1/2 Kitaev chains using specific pair pulse sequences applied to central unit cells. This method promotes long-distance spin correlations and maximal bipartite entanglement entropy. The technique is successfully extended to generalized XY chains and applied to the twisted Kitaev chain CoNb2O6, demonstrating robustness against perturbations.

Key concepts

Majorana Fermions: These are a specific type of quasiparticles used to describe the spin-1/2 Kitaev chain. They are related to complex fermions and have specific anti-commutation rules. The paper uses them to characterize the pairing between sites, which is crucial for understanding entanglement in this system.
Pair Pulse Sequence: This involves applying a carefully timed pulse sequence on the central unit cell of the chain. This action specifically modifies a conserved quantity, changing its eigenvalue to 0.5, which forces Majorana fermions at the central sites to pair together and initiate long-distance correlations.
Twisted Kitaev Chain: This is a specific model of the Kitaev chain where the quantization axis is tilted due to bond-dependent Ising interactions. The paper shows that even in this twisted version, a unitary pulse can generate entangled Majorana pairs with finite entanglement entropy, proving robustness against certain perturbations.

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This episode discusses

The paper

Creating long-range entangled Majorana pairs: from spin-1/2 twisted Kitaev to generalized XY chains · Read on arXiv

Haoting Xu, Hae-Young Kee

Department of Physics, University of Toronto · Canadian Institute for Advanced Research

Entangling a pair of far-distant qubits in many-body systems has been a challenging task in quantum computing. A robust entanglement was predicted in the rainbow states and generating nonlocal Bell pairs protected by a mirror symmetry was recently proposed. We investigate a way to create entangled Majorana fermions in the spin-1/2 Kitaev chain with open boundary conditions. The spin-1/2 Kitaev chain, a one-dimensional version of the honeycomb lattice with bond-dependent Ising interactions, has a macroscopic degeneracy related to the zero modes containing non-local spin strings. We show that applying a pair pulse sequence on the central unit cell of the chain promotes long distance spin correlations and maximal bipartite entanglement entropy. We extend this method to the generalized bond-dependent spin-1/2 chain by introducing another set of Majorana fermions and make a comparison to the entangled Bell pairs. The time to reach maximal bipartite entanglement entropy is shorter in the Kitaev chain as the zero modes do not participate in the entangled pairs. An application of our results to a recently proposed twisted Kitaev chain, CoNb2O6, is presented and future directions are also discussed.

DOI: 10.1103/PhysRevB.107.134435

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Creating long-range entangled Majorana pairs".

Mira: The gist The maximally entangled rainbow-like Majorana pairing state can be reached, with a sequence of pairing pulses applied on the central unit cell of the system.

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we've covered the "Creating long-range entangled Majorana pairs: from spin-one/two twisted Kitaev to generalized XY chains" paper today <ref:2301.10777#pg1,Creating long-range entangled Majorana pairs: from spin-1/2 twisted Kitaev>. The authors Haoting Xu and Hae-Young Kee explored how to generate these entangled Majorana fermions in the spin-one/two Kitaev chain with open boundary conditions <ref:2301.10777#pg1,entangled Majorana fermions in the spin-1/2 Kitaev chain with open>.

Mira: They focus on using a pair pulse sequence on the central unit cell of the chain to promote those long distance spin correlations and maximal bipartite entanglement entropy, extending it to generalized bond-dependent chains and connecting them to Bell pairs.

Lev: From an error correction standpoint, I see that the time scaling is something we need to keep in mind when mapping this onto real hardware constraints. And they show that for the CoNb2O6 twisted system, you can still generate those entangled Majorana pairs using a unitary pulse even if it's not maximally entangled.

Kai: So the main implication is showing a robust protocol, one that works across different chain types and handles certain perturbations reasonably well. It gives us a concrete recipe for creating these specific quantum states.

Mira: It also provides a deeper link between these Majorana pairs and Bell pairs through the complex fermion representation, which helps us understand nonlocality in these many-body systems better.

Lev: The real challenge, as always with this kind of work, is moving from the theoretical protocol to implementing it with the fidelity required for actual quantum computation. That's where our focus stays.

Conclusion: Kai: So, this paper, "Creating long-range entangled Majorana pairs: from spin-one/two twisted Kitaev to generalized XY chains," is all about showing how you can make these Majorana fermions that are far apart entangled in these complex spin chains.

Mira: Yeah, it basically takes those theoretical predictions about rainbow states and shows a concrete way to actually generate them using pairing pulses on the central part of the chain.

Lev: From my side, I’m looking at this because the Kitaev chain itself is a major model for topological quantum computation, so seeing how you build entanglement in it matters for real hardware.

Kai: Right, and they show that this method isn't just for one specific system; they take it further by generalizing it to other bond-dependent chains, like the XY model.

Mira: And the comparison they make to Bell pairs is pretty cool because it links these Majorana states directly to the nonlocality we’re trying to measure in quantum systems.

Lev: The time scaling they give for reaching maximal entanglement tells me how much overhead you'd need on a real machine before you get meaningful results, and it looks pretty good for the Kitaev chain.

Kai: It also tackles the twisted Kitaev chain, CoNb2O6, showing that even with those extra non-Kitaev interactions, you can still get those entangled Majorana pairs.

Mira: And they point out that even if it’s not perfectly maximal entanglement in every case, the state is still protected by some of that mirror symmetry we talked about before.

Lev: That robustness under perturbations is key; it means this protocol might be more resilient than we initially thought when you start messing with the physical parameters.

Kai: So, the big idea here is proving that you have a practical sequence of operations to engineer long-distance quantum correlations in these systems.

Mira: It shifts the focus from just predicting these states to actually having a recipe for their creation in various chain models.

Lev: It gives us a clearer target for what kind of control pulses we need to design if we want to build actual hardware that uses these topological properties effectively.

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