Research & Publications

Abstract: In this work, we study the sample complexity of two variants of product testing when restricted to single-copy measurements. In particular, we consider both bipartite product testing (i.e., does there exist at least one non-trivial cut across which the state is product) and multipartite product testing (i.e., is the state fully product across every cut). For the first variant, we prove an exponential lower bound on the sample complexity of any algorithm for this task which utilizes only single-copy measurements. When comparing this with known efficient algorithms that utilize multi-copy measurements, this establishes an exponential separation for this and several related entanglement learning tasks. For the second variant, we prove another sample lower bound that establishes a separation between single- and multi-copy strategies. To obtain our results, we prove a crucial technical lemma that gives a lower bound on the overlap between tensor products of permutation operators acting on subsystems of states that themselves carry a tensor structure. Finally, we provide an algorithm for multipartite product testing using only single-copy, local measurements, and we highlight several interesting open questions arising from this work.

Abstract: In this work, we study the asymptotic behavior of protocols that localize entanglement in large multi-qubit states onto a subset of qubits by measuring the remaining qubits. We use the maximal average n-tangle that can be generated on a fixed subsystem by measuring its complement -- either with local or global measurements -- as our key figure of merit. These quantities are known respectively as the localizable entanglement (LE) and the entanglement of assistance (EA). We build upon the work of [arXiv:2411.04080] that proposed a polynomial-time test, based on the EA, for whether it is possible to transform certain graph states into others using local measurements. We show, using properties of the EA, that this test is effective and useful in large systems for a wide range of sizes of the measured subsystem. In particular, we use this test to demonstrate the surprising result that general local unitaries and global measurements will typically not provide an advantage over the more experimentally feasible local Clifford unitaries and local Pauli measurements in transforming large linear cluster states into GHZ states. Finally, we derive concentration inequalities for the LE and EA over Haar-random states which indicate that the localized entanglement structure has a striking dependence on the locality of the measurement. In deriving these concentration inequalities, we develop several technical tools that may be of independent interest.

Abstract: We quantify how squeezed light can reduce quantum measurement noise to levels below the standard quantum limit in impulse measurements with mechanical detectors. The broadband nature of the signal implies that frequency-dependent squeezing performs better than frequency-independent squeezing. We calculate the optimal scaling of the impulse sensitivity with the squeezing strength, and quantify degradations due to photodetection losses. Even for lossless measurement, we find there exists a fundamental limit to the benefit of squeezing that depends only on the system's mechanical properties.

Abstract: Despite multipartite entanglement being a global property of a quantum state, a number of recent works have made it clear that it can be quantified using only local measurements. This is appealing because local measurements are the easiest to implement on current quantum hardware. However, it remains an open question what protocol one should use in order to minimize the resources required to estimate multipartite entanglement from local measurements alone. In this work, we construct and compare several estimators of multipartite entanglement based solely on the data from local measurements. We first construct statistical estimators for a broad family of entanglement measures using local randomized measurement (LRM) data before providing a general criterion for the construction of such estimators in terms of projective 2-designs. Importantly, this allows us to derandomize the multipartite estimation protocol based on LRMs. In particular, we show how local symmetric, informationally complete positive operator-valued measures enable multipartite entanglement quantification with only a single measurement setting. For all estimators, we provide both the classical postprocessing cost and rigorous performance guarantees in the form of analytical upper bounds on the number of measurements needed to estimate the measures to any desired precision.

Abstract: We give a systematic theoretical treatment of linear quantum detectors used in modern high energy physics experiments, including dark matter cavity haloscopes, gravitational wave detectors, and impulsive mechanical sensors. We show how to derive the coupling of signals of interest to these devices, and how to calculate noise spectra, signal-to-noise ratios, and detection sensitivities. We emphasize the role of quantum vacuum and thermal noise in these systems. Finally, we review ways in which advanced quantum techniques—squeezing, non-demolition measurements, and entanglement—can be or currently are used to enhance these searches..

Abstract: We show how to estimate a broad class of multipartite entanglement measures from Bell basis measurement data. In addition to lowering the experimental requirements relative to previously known methods of estimating these measures, our proposed scheme also enables a simpler analysis of the number of measurement repetitions required to achieve an ϵ-close approximation of the measures, which we provide for each. We focus our analysis on the recently introduced Concentratable Entanglements [Beckey et al. Phys. Rev. Lett. 127, 140501 (2021)] because many other well-known multipartite entanglement measures are recovered as special cases of this family of measures. We extend the definition of the Concentratable Entanglements to mixed states and show how to construct lower bounds on the mixed state Concentratable Entanglements that can also be estimated using only Bell basis measurement data. Finally, we demonstrate the feasibility of our methods by classically simulating their implementation on a noisy Rydberg atom quantum computer.

Abstract: Detecting a signal at an unknown frequency is a common task, arising in settings from dark-matter detection to magnetometry. For any detection protocol, the precision achieved depends on the frequency of the signal and can be quantified by the quantum Fisher information (QFI). To study limitations in broadband sensing, we introduce the integrated quantum Fisher information and derive inequality bounds that embody fundamental trade-offs in any sensing protocol. Our inequalities show that sensitivity in one frequency range must come at the cost of reduced sensitivity elsewhere. For many protocols, including those with small phase accumulation and those consisting of 𝜋 pulses, we find that the integrated quantum Fisher information scales linearly with 𝑇. We also find protocols with substantial phase accumulation that can have integrated QFI that grows quadratically with 𝑇 and prove that this scaling is asymptotically optimal. These protocols may allow the very rapid detection of a signal with unknown frequency over a very wide bandwidth. We discuss the implications of these results for a wide variety of contexts, including dark-matter searches and dynamical decoupling. Thus we establish fundamental limitations on the broadband detection of signals and highlight their consequences.

Abstract: The split photodiode and the lateral effect photodiode are two popular detectors for measuring beam displacement. For small displacements of a Gaussian beam, which is the case of interest here, they are often seen as equivalent and used interchangeably, giving a signal proportional to the displacement. We show theoretically and experimentally that in the limit of low technical noise, where the signal to noise ratio is dominated by the shot noise of the light, the lateral effect photodiode produces a better signal to noise ratio than the split photodiode, owing to its optimum spatial detector response. This quantum advantage can be practically exploited in spite of the intrinsic thermal noise of the lateral effect photodiode.

Abstract: The Quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state, and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed state is in general a computationally demanding task. In this work we present a variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) to address this task. By estimating lower and upper bounds on the QFI, based on bounding the fidelity, VQFIE outputs a range in which the actual QFI lies. This result can then be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. In contrast to previous approaches, VQFIE does not require knowledge of the explicit form of the sensor dynamics. We simulate the algorithm for a magnetometry setup and demonstrate the tightening of our bounds as the state purity increases. For this example, we compare our bounds to literature bounds and show that our bounds are tighter.

Abstract: In this work, we present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices. This bound itself is of interest, as we show that it satisfies the canonical criteria of a QFI measure. Specifically, it is essentially a QFI measure for subnormalized states, and hence it generalizes the standard QFI in this sense. Our bound employs the generalized fidelity applied to a truncated state, which is constructed via the m largest eigenvalues and their corresponding eigenvectors of the probe quantum state ρθ. Focusing on unitary families of exact states, we analyze the properties of our proposed lower bound, and demonstrate its utility for efficiently estimating the QFI.

Abstract: Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state, |ψ⟩, for these applications is often directly related to the degree or type of entanglement present in |ψ⟩. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called Concentratable Entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under Local Operations and Classical Communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.

Abstract: The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we analyze a lower bound on the QFI which we call the sub-Quantum Fisher Information (sub-QFI). The bound can be efficiently estimated on a quantum computer for an n-qubit state using 2n qubits. The sub-QFI is based on the super-fidelity, an upper bound on Uhlmann's fidelity. We analyze the sub-QFI in the context of unitary families, where we derive several crucial properties including its geometrical interpretation. In particular, we prove that the QFI and the sub-QFI are maximized for the same optimal state, which implies that the sub-QFI is faithful to the QFI in the sense that both quantities share the same global extrema. Based on this faithfulness, the sub-QFI acts as an efficiently computable surrogate for the QFI for quantum sensing and quantum metrology applications. Finally, we provide additional meaning to the sub-QFI as a measure of coherence, asymmetry, and purity loss.

Abstract: Nonlinear interferometers that replace beam splitters in Mach-Zehnder interferometers with nonlinear amplifiers for quantum-enhanced phase measurements have drawn increasing interest in recent years, but practical quantum sensors based on nonlinear interferometry remain an outstanding challenge. Here, we demonstrate the first practical application of nonlinear interferometry by measuring the displacement of an atomic force microscope microcantilever with quantum noise reduction of up to 3 dB below the standard quantum limit, corresponding to a quantum-enhanced measurement of beam displacement of 1.7  fm/√Hz. Further, we minimize photon backaction noise while taking advantage of quantum noise reduction by transducing the cantilever displacement signal with a weak squeezed state while using dual homodyne detection with a higher power local oscillator. This approach may enable quantum-enhanced broadband, high-speed scanning probe microscopy.

Abstract: Broadband quantum noise reduction can be achieved in gravitational-wave detectors by injecting frequency-dependent squeezed light into the dark port of the interferometer. This frequency-dependent squeezing can be generated by combining squeezed light with external filter cavities. However, in future long baseline interferometers (LBIs), the filter cavity required to achieve the broadband squeezing has a low bandwidth—necessitating a very long cavity to mitigate the issue from optical loss. It has been shown recently that by taking advantage of Einstein-Podolsky-Rosen (EPR) entanglement in the squeezed light source, the interferometer can simultaneously act as a detector and a filter cavity. This is an attractive broadband squeezing scheme for LBIs because the length requirement for the filter cavity is naturally satisfied by the length of the interferometer arms. In this paper we present a systematic way of finding the working points for this broadband squeezing scheme in LBIs. We also show that in LBIs, the EPR scheme achieves nearly perfect ellipse rotation as compared to 4-km interferometers which have appreciable error around the intermediate frequency. Finally, we show that an approximation for the optomechanical coupling constant in the 4-km case can break down for longer baselines. These results are applicable to future detectors such as the 10-km Einstein Telescope and the 40-km Cosmic Explorer.