Globally optimal interferometry with lossy twin Fock probes

• URL: http://arxiv.org/abs/2308.05871v2
• Date: Wed, 15 May 2024 21:27:36 GMT
• Title: Globally optimal interferometry with lossy twin Fock probes
• Abstract summary: We show that a method of moments readout of two quadratic spin observables $J_z2$ and $J_+2+J_-2$ is globally optimal for Dicke state probes. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Parity or quadratic spin (e.g., $J_{z}^{2}$) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock input state allow to saturate the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles, but only when the interferometer phase $\theta$ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at $\theta=0$, whereas better-than-standard quantum limit performance of the $J_{z}^{2}$ readout is restricted to an $o(\sqrt{N})$ occupation imbalance. We show that a method of moments readout of two quadratic spin observables $J_{z}^{2}$ and $J_{+}^{2}+J_{-}^{2}$ is globally optimal for Dicke state probes, i.e., the error saturates the QFI for all $\theta$. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states, showing that method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of $\theta$ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four mode state $\vert {N\over 4},{N\over 4},{N\over 4},{N\over 4}\rangle$ and its lossy counterparts, showing that an advantage for estimation of any linear function of the local MZ phases $\theta_{1}$, $\theta_{2}$ (compared to independent probing of the MZ phases by two copies of $\vert {N\over 4},{N\over 4}\rangle$) appears when more than one particle is lost.

Related papers

• Maximum Entropy Encoding of Energy-Weighted Spherical Moments [2.1503190497152453]
  We study how angular energy signals composed of non-negative Monte Carlo path samples can be compressed and reconstructed for irradiance using finite moments.<n>Experiments cover 981 Poly Haven HDRI 2K scenes and three Debevec probes.
  arXiv  Detail & Related papers  (2026-08-20T00:58:59Z)
• The exact price of local realism in CHSH experiments: a measurement-dependence-detection trade-off surface, a moiré phase-locking mechanism that saturates it, and an unmeasured fringe in the fourfold coincidence sum [0.0]
  I solve the unique detection profile $D(m)=sqrtm,h(m)$ under which a deterministic sign model reproduces the singlet exactly.<n>Surviving local accounts trade off measurement dependence against a $cos 4(a-b)$ modulation of the fourfold coincidence sum.<n>I exhibit a local mechanism -- moire phase locking -- with deterministic phase evolution and all randomness quenched in frozen offsets and flight times.
  arXiv  Detail & Related papers  (2026-08-19T13:14:52Z)
• On trace invariance and energy-dependent entanglement in muon decay [45.88028371034407]
  We revisit a proposed correction to the muon magnetic anomaly measurement.<n>We compare it with energy-binned scans reported by the Fermilab $g-2$ collaboration.
  arXiv  Detail & Related papers  (2026-08-19T12:06:54Z)
• Global Minimax Readout of a Qubit Direction [5.246986428523558]
  We determine the exact worst-direction Fisher-information cost of using a parameter-independent readout to estimate an unknown qubit direction at known Bloch-vector length $$.<n>Every fixed-local architecture, including recorded classical randomization, reduces exactly to a zero-barycenter probability measure on the Bloch ball.<n>For every full-rank qubit and every trace-balanced spectral Fisher loss, the resulting minimax problem is rigid.
  arXiv  Detail & Related papers  (2026-08-17T17:26:32Z)
• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• Universal Quantum Suppression in Frustrated Ising Magnets across the Quasi-1D to 2D Crossover via Quantum Annealing [0.0]
  competing ferromagnetic and antiferromagnetic couplings generate a sign problem provably intractable for quantum Monte Carlo at any system size.<n>We measure quantum-driven transitions at $g_cmathrmQPUin0.286,,0.210,,0.156,,0.093$ for $in1.0,,0.7,,0.5,,0.3$.
  arXiv  Detail & Related papers  (2026-03-25T13:50:52Z)
• FFT-Accelerated Auxiliary Variable MCMC for Fermionic Lattice Models: A Determinant-Free Approach with $O(N\log N)$ Complexity [52.3171766248012]
  We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems.<n>We validate our algorithm on benchmark quantum physics problems, accurately reproducing known theoretical results.<n>Our work provides a powerful tool for large-scale probabilistic inference and opens avenues for physics-inspired generative models.
  arXiv  Detail & Related papers  (2025-10-13T07:57:21Z)
• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition [46.176861415532095]
  We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions.<n>Our results exhibit a remarkable analogy to Anderson localization, with $G_AB$ corresponding to two-terminal conductance.<n>Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
  arXiv  Detail & Related papers  (2025-07-15T13:44:14Z)
• Causality, localisation, and universality of monitored quantum walks with long-range hopping [0.0]
  We show that the optimal resetting rate depends on the size of the lattice and diverges as $alphato 0$. We derive simple models reproducing the numerical results, shedding light on the interplay of long-range coherent dynamics, symmetries, and local quantum measurement processes.
  arXiv  Detail & Related papers  (2025-04-16T13:08:42Z)
• Distributed quantum multiparameter estimation with optimal local measurements [0.0]
  We study a sensor made by an array of $d$ spatially-distributed Mach-Zehnder interferometers (MZIs) We show that local measurements, independently performed on each MZI, are sufficient to provide a sensitivity saturating the quantum Cram'er-Rao bound. We find that the $d$ independent interferometers can achieve the same sensitivity of the entangled protocol but at the cost of using additional $d$ non-classical states.
  arXiv  Detail & Related papers  (2024-05-28T17:45:07Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Localization measures of parity adapted U($D$)-spin coherent states applied to the phase space analysis of the $D$-level Lipkin-Meshkov-Glick model [0.0]
  We study phase-space properties of critical, parity symmetric, $N$-quDit systems undergoing a quantum phase transition. For finite $N$, parity can be restored by projecting DSCS onto $2D-1$ different parity invariant subspaces. Pres of the QPT are then visualized for finite $N$ by plotting the Husimi function of these parity projected DSCS in phase space.
  arXiv  Detail & Related papers  (2023-02-13T10:51:19Z)
• A Law of Robustness beyond Isoperimetry [84.33752026418045]
  We prove a Lipschitzness lower bound $Omega(sqrtn/p)$ of robustness of interpolating neural network parameters on arbitrary distributions. We then show the potential benefit of overparametrization for smooth data when $n=mathrmpoly(d)$. We disprove the potential existence of an $O(1)$-Lipschitz robust interpolating function when $n=exp(omega(d))$.
  arXiv  Detail & Related papers  (2022-02-23T16:10:23Z)
• Multiparameter simultaneous optimal estimation with an SU(2) coding unitary evolution [5.789743084845758]
  In a ubiquitous $SU(2)$ dynamics, achieving the simultaneous optimal estimation of multiple parameters is difficult. We propose a method, characterized by the nested cross-products of the coefficient vector $mathbfX$ of $SU(2)$ generators. Our work reveals that quantum control is not always functional in improving the estimation precision.
  arXiv  Detail & Related papers  (2022-02-08T06:05:20Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Extreme expected values and their applications in quantum information processing [7.4733340808812505]
  We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value. We apply the proved theory to solve three problems in quantum information processing.
  arXiv  Detail & Related papers  (2021-10-31T11:10:39Z)
• Stochastic behavior of outcome of Schur-Weyl duality measurement [45.41082277680607]
  We focus on the measurement defined by the decomposition based on Schur-Weyl duality on $n$ qubits. We derive various types of distribution including a kind of central limit when $n$ goes to infinity.
  arXiv  Detail & Related papers  (2021-04-26T15:03:08Z)
• Heisenberg-limited estimation robust to detector inefficiency in a multi-parameter Mach-Zehnder network with squeezed light [0.0]
  A simple and intuitive geometrical picture of the state evolution is provided by the Wigner functions of the state at each interferometer output channel. The protocol allows to detect the value of the sum $beta=frac12(varphi_2)+theta_mathrmin-theta_mathrmout$.
  arXiv  Detail & Related papers  (2021-04-06T10:46:29Z)
• A Random Matrix Analysis of Random Fourier Features: Beyond the Gaussian Kernel, a Precise Phase Transition, and the Corresponding Double Descent [85.77233010209368]
  This article characterizes the exacts of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$ is all large and comparable. This analysis also provides accurate estimates of training and test regression errors for large $n,p,N$.
  arXiv  Detail & Related papers  (2020-06-09T02:05:40Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)
• Non-Hermitian and Zeno limit of quantum systems under rapid measurements [0.0]
  We find a scaling collapse in $F(t)$ with respect to $tau$ and compute the total detection probability as well as the moments of the first detection time probability density $F(t)$ in the Zeno limit. We show that both solutions approach the same result in this small $tau$ limit, as long as the initial state $| psi_textin rangle$ is not parallel to the detection state.
  arXiv  Detail & Related papers  (2020-05-01T15:59:13Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.