Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states (0811.4350v2)

Abstract: The concept of entanglement, in which coherent quantum states become inextricably correlated, has evolved from one of the most startling and controversial outcomes of quantum mechanics to the enabling principle of emerging technologies such as quantum computation and quantum sensors. The use of entangled particles in measurement permits the transcendence of the standard quantum limit in sensitivity, which scales as N^1/2 for N particles, to the Heisenberg limit, which scales as N. This approach has been applied to optical interferometry using entangled photons and spin pairs for the measurement of magnetic fields and improvements on atomic clocks. Here, we demonstrate experimentally an 9.4-fold increase in sensitivity to an external magnetic field of a 10-spin entangled state, compared with an isolated spin, using nuclear spins in a highly symmetric molecule. This approach scales in a favourable way compared to systems where qubit loss is prevalent, and paves the way for enhanced precision in magnetic field sensing

• The paper demonstrates a 9.4-fold sensitivity boost in magnetic field detection using 10-spin entangled NOON states.
• It employs a trimethyl phosphite molecule with controlled Hadamard and CNOT operations on nuclear spins to achieve high precision.
• The study highlights that spin-based NOON states are more resilient to dephasing noise, paving the way for practical quantum sensors.

An Overview of Magnetic Field Sensing Beyond the Standard Quantum Limit Using 10-Spin NOON States

The research presented in this paper investigates quantum enhancement of magnetic field sensing using 10-spin entangled NOON states. This work extends the understanding of quantum enhancements in sensitivity, particularly in the context of NOON states constructed with nuclear spins. These states utilize quantum entanglement to overcome the standard quantum limit, achieving higher sensitivity levels potentially beneficial for practical quantum sensors.

Key Contributions

• NOON States and Sensitivity Enhancement: By employing 10-spin NOON states, this paper demonstrates a substantially increased sensitivity to magnetic fields compared to classical fields. Specifically, a 9.4-fold enhancement in sensitivity was observed compared to a single unentangled nucleus. This is achieved through the superposition and entanglement inherent in NOON states, which underpin their superior sensitivity by allowing phase accumulation at a rate proportional to the number of particles, shifting from the $\sqrt{N}$ scaling of unentangled particles towards the Heisenberg limit of $N$ scaling.
• Experimental Realization Using Nuclear Spins: The experimental setup utilizes a trimethyl phosphite molecule as a testbed, consisting of one $^{31}$P spin and nine $^1$H nuclear spins interacting in a star-like topology. This configuration is optimal for creating nuclear spin-NOON states and exploring their phase sensitivity through controlled quantum operations, including Hadamard and controlled-NOT gates applied to spin qubits.
• Versatility in Noise Conditions: The paper provides insights into the resilience of spin-NOON states against dephasing noise, contrasting it with optical NOON states that are vulnerable to photon loss. This increased robustness to noise positions spin-based NOON states as more feasible for real-world sensor implementations where phase stability is critical.

Theoretical and Practical Implications

The findings have multiple implications for the field of quantum technologies. From a theoretical standpoint, this demonstrates the capabilities and limits of quantum enhancement in measurement precision, providing a blueprint for achieving Heisenberg-limited sensitivity in quantum systems. Practically, the implementation of nuclear spin-based systems in magnetic field sensing provides a path forward for developing next-generation sensor technologies potentially applicable in numerous scientific and industrial fields.

Future Directions

Future research may focus on scaling these methods to larger entangled systems to further explore the quantum advantages in sensitivity. Additionally, harnessing dynamic nuclear polarization or algorithmic cooling might help overcome current limitations in nuclear spin initialization, thereby enhancing practical applications. The adaptation of this method to electron spins and their integration into nanometer-scale devices could precipitate breakthroughs in nanoscale sensing technologies.

This paper thus significantly advances the domain of quantum sensing, enriching both theoretical understanding and paving the way for innovative practical applications in quantum-enhanced magnetic field sensing.