Quantum entanglement is one of the most well-studied phenomena in quantum physics. Einstein called it “spooky action at a distance,” as it enables particles to be deeply connected—such that measuring one instantly reveals information about the other, regardless of the distance between them. For decades, quantum entanglement has been used to design protocols for studying other physical processes, including quantum teleportation, which allows the transfer of quantum states without physically moving particles.
While quantum teleportation has been experimentally demonstrated in various settings, including individual photons and ions, extending this protocol to many-body systems—composed of many interacting particles—has remained a significant theoretical challenge. In contrast to isolated particles, many-body systems feature complex interdependencies where quantum information is shared across the entire ensemble. These collective behaviors give rise to rich dynamics and entanglement structures that are essential for quantum technologies but also introduce a level of complexity that makes teleportation more difficult to design and implement.
Now, in a recent study published in Physical Review Research, researchers at JILA—led by JILA and NIST Fellow and University of Colorado Boulder physics professor Ana Maria Rey and her team, along with Klaus Molmer from the Neils Bohr Institute and John Bollinger from NIST—have developed a new protocol for teleporting quantum information stored in collective spin states of ions within a two-dimensional crystal. This approach bridges concepts from atomic physics, quantum optics, and quantum information science, opening new avenues for building modular, scalable systems for quantum information processing.
“Fundamentally, we Einstein-Podolsky-Rosen correlations—entanglement—between collective spin systems, using tools experimentally accessible in trapped ions,” explains theorist Muhammad Miskeen Khan, who recently completed his postdoc from JILA and is now a postdoctoral researcher at Saint Louis University. “Then came up with a protocol that used that entanglement as a resource to teleport many-body collective spin states between energetically distinct ensembles.”
“Our proposed teleportation protocol leverages both phonon-mediated collective spin-spin interactions among three energetically separated spin-ensembles in a two-dimensional trapped ions crystal together with measurements and local operations on these ensembles,” Rey says. “We have taken advantage of different nuclear spin levels accessible in the system. Although in the current proposal the suggested protocol depends on spin ensembles that are energetically separated but spatially overlapping, future advancements could be gained from implementing our proposed protocols in spatially separated ensembles, for example, using 3D ion crystals.”
From Individual Ions to Collective Spin Ensembles
In quantum experiments, spin refers to the internal angular momentum of particles such as electrons or atomic nuclei. Like each goose in a flock facing one direction so that the whole flock is facing the same direction, in a system of many atoms, their spins can be treated as a collective spin—a combined property that captures the net behavior of the ensemble. Such collective spin states are helpful in precision measurements and quantum computing, especially when they exhibit quantum correlations such as squeezing or entanglement.
The JILA team designed a teleportation protocol in which these collective states—rather than individual ions—are transferred between ion subgroups within a Penning trap, a system used to trap large systems of ions via a set of electrodes and a strong magnetic field. The system they studied consists of a 2D array of trapped beryllium ions in a crystal, which vibrate coherently through shared vibrations, or phonon modes, which can be used to individually manipulate nuclear and electronic spin states of these ions by driving them with lasers and microwave fields. Instead of spatially separated ion ensembles, the researchers separated the ensembles by using distinct nuclear spin levels (or internal ion levels) within the crystal, which have large energy splittings in the strong magnetic field used in the Penning trap to confine the ions. The investigators used three levels to emulate three independent quantum subsystems: Alice, Bob, and Charlie.
First, Alice and Bob—two ion groups—are linked together through a phonon mode of the entire crystal. This phonon mode acts like a mediator, allowing the spins in Alice and Bob to become entangled and form a correlated quantum state.
Next, the third sub-ensemble or nuclear spin energy level, Charlie, holds a quantum state that the researchers want to teleport. This state is gently combined with Alice’s state to mix their information coherently without measuring it directly—like blending two sound waves before analyzing them.
Finally, both Alice and Charlie quantum states are measured. These measurements don't reveal the full quantum state but provide enough information, which is sent to adjust Bob’s group to end up in the same quantum state that Charlie originally had. The result is that Charlie’s state appears in Bob’s ions, effectively teleporting the quantum information across the system.
The protocol, adapted from continuous-variable teleportation schemes in quantum optics, was successfully numerically simulated in systems containing up to 300 ions per ensemble. The simulation also showed the possibility of achieving a high-fidelity teleportation of classical and non-classical spin states, including spin-coherent, spin-squeezed, and Dicke states, under current experimental conditions. Spin-squeezed and Dicke states are particularly interesting because they exhibit entanglement and are helpful for quantum-enhanced sensing, quantum information processing, and computation.
Demonstrating the teleportation of these states suggests that the protocol could one day serve as a mechanism for distributing entanglement and quantum information processing in quantum networks of ions.
“Typically, teleportation circuits are applied to spin-coherent states, which are relatively easy to prepare and simulate,” Khan notes. “We showed that the same protocol can be extended to non-trivial, entangled states, which had not been clearly demonstrated before in a collective spin setting.”
This theoretical protocol is also experimentally realistic. The proposed platform leverages existing techniques in Penning traps, where ion crystals are cooled, entangled, and interrogated with a high degree of control. The phonon modes in the trap are long-lived, robust to noise, and capable of coupling hundreds of ions simultaneously, making them ideal for entanglement distribution.
Protocols with Many Applications
Teleportation protocols like these could serve as building blocks for special types of quantum devices, where quantum information is moved from one register to another without physical transport. It also lays the groundwork for distributed quantum sensing, where entangled states are shared across separate sensors to improve measurement precision.
Beyond practical applications, this work could be the starting point for implementing schemes relevant to simulating quantum gravity in the lab and quantum information scrambling.
“Currently, we are working on some quantum information protocols implementable in the NIST Penning trap inspired by black hole physics,” JILA graduate student Edwin Chaparro says. “Black holes are believed to be the fastest-scrambling objects in nature. We want to leverage the capability to generate scrambling in ion arrays to perform quantum teleportation and information recovery protocols and quantum metrology applications.”
Looking ahead, the researchers hope to extend the protocol to spatially separated systems, potentially using a new generation of trapped ion crystals that live in three special dimensions instead of two. They also plan to explore how similar schemes could be implemented in other physical platforms, such as neutral atom arrays or polar molecules.
This work was supported by the U.S. Department of Energy’s Office of Science, National Quantum Information Science Research Centers, the Quantum Systems Accelerator, the JILA Physics Frontier Center, and NIST.
Written by Kenna Hughes-Castleberry, JILA Science Communicator
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