Quantum Precision Survives Particle Loss Thanks to Information Scrambling Techniques

Scientists have long sought to harness entanglement to enhance measurement precision, but this advantage is typically fragile and diminishes as particles are lost. Now, research led by Piotr Wysocki of the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences and University of Innsbruck, alongside Jan Chwedeńczuk from the Faculty of Physics, University of Warsaw, and Marcin Płodzień from Qilimanjaro Quantum Tech, reveals how ‘scrambling’ can protect this precision by distributing information across many-body correlations. Their work demonstrates a clear threshold whereby retaining a sufficiently large subsystem, above a critical size, allows full recovery of the quantum Fisher information, effectively safeguarding metrological advantage. This finding links the resilience of precision to the transition from area-law to volume-law entanglement, offering a crucial step towards robust quantum sensing and computation.

Scrambling dynamics and many-body correlations preserve quantum precision with particle loss

Scientists have demonstrated that scrambling dynamics safeguard metrological precision against particle loss in quantum systems. This work reveals a threshold whereby retaining a subsystem exceeding half the original size preserves the full quantum Fisher information, a key metric for precision measurements.
Researchers derived exact formulas describing how information disperses into many-body correlations during scrambling, effectively protecting encoded parameters even as particles are lost. The study establishes a link between scrambling-induced transitions from area-law to volume-law entanglement and the growth of the Schmidt rank, offering a novel approach to quantum information preservation.

This breakthrough addresses a fundamental challenge in quantum metrology, where even minor particle loss can destroy the enhanced sensitivity achieved through entanglement. The research demonstrates that scrambling, a process of state-rank growth under unitary evolution, disperses information, preventing its degradation due to particle erasure.

Through Haar-random scrambling unitaries, the team obtained analytical formulas for the average quantum Fisher information of a reduced state after particles are traced out. These formulas reveal that any remaining subsystem larger than N/2, half the original number of particles, retains the full quantum Fisher information, while smaller subsystems contain negligible information.

The findings connect to quantum error correction, as particle loss represents an erasure error, and random encoders prove nearly optimal in this scenario. Researchers identified that the locking of the quantum Fisher information arises from an increase in the Schmidt rank and a transition from area-law to volume-law entanglement.

Two specific realizations of this protection were outlined: a brickwork circuit and chaotic XX-chain evolution, both demonstrating the ability to safeguard one-axis-twisted probes against the loss of up to half the particles. Furthermore, the study proposes experimental protocols for implementing this information locking in digital and analogue quantum simulators.

Specifically, scrambling unitaries are applied to initial states, and the technique is demonstrated using entangled states generated via the one-axis twisting protocol and a chaotic XX spin chain with random transverse fields, a system readily implementable in existing quantum simulators. The study begins by encoding a parameter θ within a pure state |ψ(θ)⟩, subsequently applying a global scrambling unitary U to generate a scrambled state |ψ(U)(θ)⟩.

This scrambled state undergoes bipartitioning, expressed as |ψ(U)(θ)⟩ = U|ψ(θ)⟩ = dA X i=1 ci|αi⟩⊗|βi⟩, where |αi⟩ belong to subsystem A and |βi⟩ to subsystem B, with dA representing the dimension of HA and being less than or equal to the dimension of HB. This averaging yields analytical expressions that are compared against the initial QFI, Iq [ρ(θ)], revealing the extent of information retained after scrambling and particle loss.

To further elucidate information spreading, the study utilizes Page’s theorem, demonstrating that the reduced state of the smaller subsystem A becomes nearly maximally mixed, with eigenvalues approximately equal to d−1A. This leads to the approximation ρ(U) A (θ) ≈1 dA 1A and ρ(U) B (θ) ≈1 dA Π(U) B, where Π(U) B is a projector onto the subspace of HB.

The QFI for subsystem A is then approximated as Iq h ρ(U) A i ≈dAtrA ρ(U) A 2, and the SWAP-trick is employed to express the trace over H⊗2 as tr[( X⊗Y ) S]. Averaging over all unitary matrices using Weingarten calculus results in a compact expression, Eμ(U) h Iq h ρ(U) A ii = Iq [ρ(θ)] × fA, where fA is a rational function dependent on dA and dB.

Quantum information survives particle loss via entanglement transition and scrambling

Logical error rates of 2.9% per cycle have been achieved through a scrambling process that safeguards precision against particle loss. This work demonstrates that dispersing information about an encoded parameter into many-body correlations protects quantum information. Researchers derived exact formulas for the average Fisher information (QFI) of the reduced state following the tracing out of lost particles, revealing a critical threshold for information retention.

Any remaining subsystem exceeding this threshold recovers the full QFI, while smaller subsystems contain negligible information. The study links this threshold to the transition from area-law to volume-law entanglement induced by scrambling, alongside the associated growth of the Schmidt rank. Two realizations were outlined: a brickwork circuit and chaotic XX-chain evolution, both demonstrating protection of one-axis-twisted probes against the loss of up to 50% of the particles.

Analytical predictions, expressed by equations and, closely match numerical results obtained from simulating systems of up to N qubits, confirming the robustness of the findings. The research establishes that complementary subsystems retain the full QFI when scrambling locks the encoded information into volume-law correlations, meaning any subsystem retaining more than half the particles recovers the full QFI.

Initial states, encoded via the generator G = 1/2 Σi σx i, yielded a pure-state QFI value of N. Following scrambling with a Haar-random unitary, the QFI of the reduced density matrix, obtained by tracing out K qubits where K ranges from 0 to N, remained largely preserved. Analysis of bipartite entanglement entropy reveals that shallow circuits (L ≪ N) and short evolution times result in area-law states, while deeper circuits (L ≥ N/2) and longer evolution times produce states following volume-law entanglement scaling. This transition demonstrates that scrambling transforms fragile low-rank coherence into a high-rank state, spreading encoded information uniformly across all degrees of freedom and protecting the QFI against particle loss.

Quantum information resilience via entanglement transition in lossy systems

Scrambling dynamics represent a robust mechanism protecting quantum-enhanced metrological information from particle loss. Researchers have derived exact formulas for the average quantum Fisher information retained in a reduced state after particles are lost, utilising Haar-random scrambling unitaries.

These calculations reveal a critical threshold whereby subsystems containing more than half of the original particles preserve the full quantum Fisher information, while smaller subsystems exhibit negligible information content. This preservation arises from a transition occurring during scrambling from area-law to volume-law entanglement, effectively dispersing information about the encoded parameter across numerous degrees of freedom.

Two experimentally viable protocols, a brickwork circuit and chaotic XX-chain evolution, were outlined and demonstrated to maintain near-optimal metrological advantage even with the loss of up to half the particles. The findings also indicate that scrambling dynamics can safeguard quantum-enhanced sensitivity against erasure errors, offering a pathway towards fault-tolerant quantum sensing.

The authors acknowledge a limitation in that their analysis relies on the approximation of Haar-random scrambling, and future work could explore the performance of more practical scrambling implementations. Further research will focus on applying these principles to platforms susceptible to particle loss, including atomic ensembles, photonic networks, and noisy intermediate-scale quantum devices, ultimately advancing the development of robust quantum sensing technologies.