Supraclassical measurement using single-atom control of an atomic ensemble

Abstract

We analyze the operation of a sensor based on atom interferometry, which can achieve supraclassical sensitivity by exploiting quantum correlations in mixed states of many qubits. The interferometer is based on quantum gates which use coherently controlled Rydberg interactions between a single atom (which acts as a control qubit) and an atomic ensemble (which provides register qubits). In principle, our scheme can achieve precision scaling with the size of the ensemble-which can extend to large numbers of atoms-while using only single-qubit operations on the control and bulk operations on the ensemble. We investigate realistic implementation of the interferometer, and our main aim is to develop an approach to quantum metrology that can achieve quantum-enhanced measurement precision by exploiting coherent operations on large impure quantum states. We propose an experiment to demonstrate the enhanced sensitivity of the protocol and to investigate a transition from classical to supraclassical sensitivity which occurs when using highly mixed probe states.

Noisy frequency estimation with noisy probes

“…The overall initial state is the product Here, l ( ) i 0 and l ( ) i 1 are the probabilities of the ith qubit being in state ñ |0 and ñ |1 , respectively. This setup could describe an experiment which senses magnetic or gravitational fields using an ensemble of atoms [20,39]. Such an ensemble can be initially aligned with the direction an external magnetic field so that the Bloch vector of each qubit will be pointing in the same direction.…”

“…where  k is defined in equation (20). To calculate the total CFI, one has to sum over all possible strings of measurement outcomes, characterised by k: Here,   C is the time-optimised CFI, with optimal time for the correlated probes denoted by t é .…”

“…The observations of these experiments are explained by the calculations of [18], where it is shown that correlations (that may be weaker than entanglement) can lead to a quadratic enhancement in the sensitivity. Expanding on the same ideas, [19] (also see the experimental proposal [20]) made use of ideas from the computational model called deterministic quantum computation with one bit of quantum information (DQC1) [21] to show that using n maximally mixed qubits, along with one pure qubit, is sufficient to saturate the classical limit to sensing. On the other hand, [22,23] showed that the figure of merit in metrology reduces to a measure of quantum discord [24,25] when there is lack of knowledge about the generator of the parameter.…”

“…Expanding on the same ideas, Ref. [19] (also see the experimental proposal [20]) made use of ideas from the computational model called deterministic quantum computation with one bit of quantum information (DQC1) [21] to show that using n maximally mixed qubits, along with one pure qubit, is sufficient to saturate the classical limit to sensing. On the other hand, Refs.…”

Blueprint for fault-tolerant quantum computation with Rydberg atoms

“…The fidelity of the process is dependent upon the chosen atom species, Rabi frequencies and Rydberg states, but to give an indication, [25] calculated that EIT can be used to perform the operation |+000 → 1/ √ 2(|0000 + |1111 ) with a fidelity in excess of 97% with 87 Rb. Higher fidelities may be achieved by an appropriate choice of the laser parameters and Rydberg states, as discussed in [26] and [27], where the gating parameters were optimized for different spatial arrangements of the target qubits. Fidelities alone don't provide details of the underlying error Figure 3: Measuring a star operator using a multi-target EIT CNOT gate.…”