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arXiv:2204.07538 · Physical Review A

Deterministic preparation of supersinglets with collective spin projections

Ebubechukwu O. Ilo-Okeke, Yangxu Ji, Ping Chen, Yuping Mao, Manikandan Kondappan, Valentin Ivannikov, Yanhong Xiao, Tim Byrnes

Published Sep 16, 2022• 9 citations
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Abstract

We introduce a procedure to generate supersinglets, the multipartite generalization of angular momentum singlet states. A supersinglet is defined as a total spin zero state consisting of $N$ spin-$j$ particles. They are highly entangled and have zero spin variance in any direction, and as such are potentially useful for quantum metrology. Our scheme is based on projective measurements that measure the collective spin of the whole spin ensemble. A local unitary rotation is applied conditionally on the measurement outcome, such as to maximize the probability of obtaining spin zero on the subsequent measurement. The sequence is repeated in the $z$ and $x$ basis until convergence is obtained towards the supersinglet state. Our sequence works regardless of the initial state, and no postselection is required. Due to the use of strong projective measurements, very fast convergence towards zero spin variance is obtained. We discuss an example implementation using quantum nondemolition measurements in atomic ensembles, and perform numerical simulations to demonstrate the procedure.

DOI
10.1103/physreva.106.033314

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We introduce a procedure to generate supersinglets, the multipartite generalization of angular momentum singlet states. A supersinglet is defined as a total spin zero state consisting of NNN spin-jjj particles. They are highly entangled and have zero spin variance in any direction, and as such are potentially useful for quantum metrology. Our scheme is based on projective measurements that measure the collective spin of the whole spin ensemble. A local unitary rotation is applied conditionally on the measurement outcome, such as to maximize the probability of obtaining spin zero on the subsequent measurement. The sequence is repeated in the zzz and xxx basis until convergence is obtained towards the supersinglet state. Our sequence works regardless of the initial state, and no postselection is required. Due to the use of strong projective measurements, very fast convergence towards zero spin variance is obtained. We discuss an example implementation using quantum nondemolition measurements in atomic ensembles, and perform numerical simulations to demonstrate the procedure.
We introduce an entanglement distillation (purification) protocol for supersinglet states composed of N qubits. The supersinglet state we target is a total spin zero state with zero spin variance, and has a fully entangled structure involving all qubits. In our distillation protocol, three copies of an initial spin zero state are measured in the local total spin basis such that a higher fidelity supersinglet state is generated upon postselection. The initial state can be prepared using conventional Bell state distillation methods distributed in a way to target the supersinglet symmetries. The protocol uses only local operations and classical communications, and is suitable for long-distance applications such as quantum clock synchronization and cryptography, and avoids a high dimensional Schur transform such that it can be used for tasks such as quantum metrology.
We develop a scheme to prepare a macroscopic maximally entangled state (MMES) between two atomic ensembles using adaptive quantum nondemolition (QND) measurements. The quantum state of the system is evolved using a sequence of QND measurements followed by adaptive unitaries, such that the desired measurement outcome is obtained with asymptotically unit probability. This procedure is repeated in z and x spin basis alternately such that the state converges deterministically towards the maximally entangled state. Up to a local spin-basis rotation, the maximally entangled state has zero total spin angular momentum, i.e. it is a singlet state. Our protocol does not perform postselection and works beyond the Holstein-Primakoff regime for the atomic spin degrees of freedom, producing genuine macroscopic entanglement.
Multipartite systems of high-dimensional particles can host forms of quantum entanglement inaccessible to qubit systems. A particularly fascinating class is formed by the fully antisymmetric states, also known as supersinglets, which possess a remarkable symmetry: they are invariant under arbitrary collective local unitaries. Here, we explore their entanglement properties and establish their quantum information applications. Using convex optimisation, we show that central entanglement features of supersinglets are remarkably robust to noise, substantially surpassing the robustness of several paradigmatic entangled states under certain relaxations. We then develop witness methods, based on collective-spin or randomised measurements, that certify both the depth and dimensionality of their entanglement. Finally, we identify supersinglets as a natural resource for high-dimensional gradient sensing and prove that they enable Heisenberg scaling. Together, these results reveal supersinglets as an exceptionally robust and versatile class of multipartite entangled states, combining striking symmetry and strong entanglement with concrete potential for quantum sensing.
We develop a scheme to prepare a macroscopic maximally entangled state between two atomic ensembles using adaptive quantum nondemolition (QND) measurements. The quantum state of the system is evolved using a sequence of QND measurements followed by adaptive unitaries such that the desired measurement outcome is obtained with asymptotically unit probability. This procedure is repeated in zzz- and xxx-spin bases alternately such that the state converges deterministically towards the maximally entangled state. Up to a local spin-basis rotation, the maximally entangled state has zero total spin angular momentum, i.e., it is a singlet state. Our protocol does not perform postselection and works beyond the Holstein-Primakoff regime for the atomic spin degrees of freedom, producing genuine macroscopic entanglement.
Ultimate quantum fluctuations which limit the fundamental precision in metrology can be only reduced by entanglement of particles. In particular, squeezing of the fluctuations called the spin projection noise by means of generation of entanglement in an ensemble of atoms can improve the precision of spectroscopy and of atomic clocks. A powerful tool for generation of multiparticle entanglement is a quantum nondemolition measurement (QND). We will describe the fundamentals of QND measurement of atomic collective state with light and present a recent experiment [1] where this method has been used to reduce the projection noise on the clock transition in an ensemble of 105 cold and trapped Cesium atoms. Another method for generation of spin squeezing via electron-nucleus entanglement applicable only for atoms with angular momentum higher than ½ will be also discussed [2].
We show that dynamic spin polarization by collective raising and lowering operators can drive a spin ensemble from arbitrary initial state to many-body singlets, the zero-collective-spin states with large-scale entanglement. For an ensemble of NNN arbitrary spins, both the variance of the collective spin and the number of unentangled spins can be reduced to O(1)O(1)O(1) [versus the typical value of O(N)O(N)O(N)], and in the steady state many-body singlets are occupied with a population of  ~ 2020%20 independent of the ensemble size. We discuss a potential implementation in a mesoscopic ensemble of nuclear spins using dynamic nuclear spin polarization by an electron. The result is of twofold significance for spin quantum technology: (1) a cleaner surrounding and less quantum noise for the electron spin and (2) a resource of entanglement for nuclear-spin-based quantum information processing. The scheme can also be applied to other spin systems where collective raising and lowering operations are available.