Quantum Leaps in Control Break Limits of Classical Physics by 50 Percent

Nuclear spins represent a promising avenue for investigating quantum correlations and the dynamics of open quantum systems, with implications for information science, foundational physics and many-body problems. Arijit Chatterjee, from the Indian Institute of Science Education and Research Pune, alongside Arijit Chatterjee and colleagues, demonstrate significant advances in this field through a series of experiments utilising a three-qubit nuclear spin register. Their research details the experimental realisation of superposed unitary dynamics exhibiting Leggett-Garg inequality violations exceeding classical bounds, alongside a novel method for determining Lee-Yang zeros using a single probe. Furthermore, they provide both theoretical and experimental verification of the Mpemba effect in nuclear spin relaxation and clarify apparent violations of the data processing inequality, offering crucial insights into entanglement dynamics and the limits of quantum information processing.

Nuclear spin qubits demonstrate enhanced non-classicality and decoherence resilience

Researchers have achieved a significant advance in manipulating and understanding quantum systems using nuclear spins, demonstrating enhanced control over quantum correlations and open system dynamics. This work centers on leveraging the unique properties of nuclear spins, specifically their extended coherence times and precise control via radio frequency pulses, to explore fundamental aspects of quantum mechanics and potentially revolutionize quantum technologies.
A three-qubit register was utilized to experimentally realize superposed unitary operators, resulting in violations of the Leggett-Garg inequality exceeding the established maximal bound of 1.5. This observation confirms enhanced non-classicality and, crucially, reveals improved robustness against decoherence, a major obstacle in quantum computation.

Further extending these capabilities, the study introduces a novel method for determining the complete set of Lee-Yang zeros, critical points revealing behavior near phase transitions, within an asymmetric Ising model. Employing a single probe qubit within the same three-qubit nuclear spin register, researchers demonstrated a direct correlation between the probe’s mutual information and the location of these Lee-Yang zeros in the complex plane.

This innovative approach offers a new pathway for characterizing complex systems and understanding their critical behavior. The research also details an experimental verification of the Mpemba effect in nuclear spin relaxation, where systems initially farther from equilibrium can exhibit faster relaxation rates than those closer to steady state.

Beyond these core findings, the study investigates entanglement localization and delocalization induced by local interactions, initially appearing to violate the data processing inequality. Through the construction of a completely positive and trace preserving map, researchers clarified that this apparent violation is not fundamental, providing a deeper understanding of entanglement dynamics. These combined advancements demonstrate the potential of nuclear spin registers as a versatile platform for probing quantum phenomena and developing future quantum technologies, offering a pathway towards more robust and efficient quantum information processing.

Leggett-Garg inequality violation and Lee-Yang zero determination via superposed unitary dynamics

Researchers utilized a three-qubit nuclear spin register to investigate temporal correlations, specifically employing the Leggett-Garg inequality (LGI) to quantify these effects in a qubit subjected to superposed unitary operators. Superposed unitary dynamics were experimentally achieved, and violations of the LGI exceeding the maximal classical bound of 1.5 were observed, demonstrating enhanced non-classical behaviour.

This work further revealed that the implemented superposed unitary dynamics exhibited improved resilience against decoherence, a crucial aspect for maintaining quantum information. Subsequently, the study focused on Lee-Yang zeros, which are critical points in the complex plane indicating system behaviour near criticality.

A novel methodology was proposed and experimentally validated using the same three-qubit register to determine the complete set of Lee-Yang zeros for an asymmetric Ising model. Measurements of mutual information between a quantum probe and the system revealed peak values at time points corresponding to these zeros, highlighting a direct correlation between spin coherence and the location of these critical points.

The sampling of the coamoeba, a visual representation of the Lee-Yang zeros, was achieved through careful preparation of the quantum probe and subsequent analysis of the resulting spin coherence. Investigations then extended to the quantum Mpemba effect in nuclear spin relaxation, where systems initially far from equilibrium were shown to relax faster than those closer to steady state.

Theoretical predictions of this effect were verified through experiments conducted on nuclear spins, eliminating the influence of dephasing to isolate the genuine Mpemba effect. High-temperature dipolar relaxation was also examined to further understand the dynamics of this phenomenon. Finally, the research addressed entanglement localization and delocalization induced by local interactions, leading to an apparent violation of the quantum data processing inequality. Through the construction of a completely positive and trace-preserving map, it was demonstrated that this violation was merely apparent, clarifying the underlying quantum dynamics and ensuring consistency with established principles.

Enhanced non-classical correlations, Lee-Yang zeros and the Mpemba effect in a three-qubit nuclear spin register

Leggett Garg inequality violations exceeding 1.5 were experimentally observed using a three-qubit register undergoing superposed unitary dynamics. This result indicates enhanced non-classical correlations within the system and demonstrates improved robustness against decoherence effects. The study successfully realised superposed unitaries, allowing for detailed investigation of temporal correlations.

Investigation of the asymmetric Ising model revealed the full set of Lee Yang zeros using a single probe within a three-qubit nuclear spin register. Mutual information between the probe and the system peaked at times directly corresponding to the locations of these zeros, providing a novel method for their determination.

This approach offers a new pathway for characterising behaviour near criticality in complex systems. The Mpemba effect in nuclear spin relaxation was both theoretically verified and experimentally demonstrated using nuclear magnetic resonance. Results confirmed instances where systems initially farther from equilibrium relaxed at a faster rate than those closer to steady state, challenging conventional expectations.

This observation expands understanding of non-equilibrium dynamics in spin systems. Entanglement localization and delocalization induced by local interactions led to an apparent violation of the data processing inequality. Construction of a completely positive and trace preserving map accurately described the observed dynamics, resolving the apparent violation and confirming the underlying principles of quantum information processing. This work clarifies the behaviour of entanglement under local interactions.

Leggett-Garg violations, Lee-Yang zeros and mutual information in a three-qubit system

Nuclear spins offer a robust system for investigating correlations and dynamics relevant to information theory, fundamental physics, and many-body systems due to their extended coherence and precise controllability. Investigations utilising a three-qubit register have demonstrated violations of the Leggett-Garg inequality exceeding established classical limits, suggesting enhanced non-classical behaviour and improved resilience to decoherence.

These experiments involved the realisation of superposed unitary operators, showcasing a novel approach to manipulating quantum states. Further research focused on the identification of Lee-Yang zeros, critical points in a system’s behaviour, by employing a single probe qubit within the same three-qubit register and an asymmetric Ising model.

The team successfully mapped the complete set of these zeros and observed a correlation between their location and peaks in mutual information between the probe and the system. Additionally, the Mpemba effect, where relaxation rates can unexpectedly increase with initial distance from equilibrium, was both theoretically modelled and experimentally verified in nuclear spin relaxation.

Finally, apparent violations of the data processing inequality were observed in entanglement dynamics, but were subsequently explained through the construction of a valid quantum map describing the system’s evolution. These findings collectively advance understanding of non-classical correlations, critical phenomena, and open quantum system dynamics.

The authors acknowledge that the observed effects are specific to the chosen experimental parameters and system size. Future work may involve extending these investigations to larger systems and exploring the potential applications of these phenomena in quantum technologies.