Bounding the fidelity of quantum many-body states from partial information

Abstract

We formulate an algorithm to lower bound the fidelity between quantum many-body states only from partial information, such as the one accessible by few-body observables. Our method is especially tailored to permutationally invariant states, but it gives nontrivial results in all situations where this symmetry is even partial. This property makes it particularly useful for experiments with atomic ensembles, where relevant many-body states can be certified from collective measurements. As an example, we show that a ${\xi }^2\approx -6\text{dB}$ spin squeezed state of $N=100$ particles can be certified with a fidelity up to $F=0.999$, only from the measurement of its polarization and of its squeezed quadrature. Moreover, we show how to quantitatively account for both measurement noise and partial symmetry in the states, which makes our method useful in realistic experimental situations.

arXiv commentcomments are welcome

References in corpus (31)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Concentrating Partial Entanglement by Local Operations
• Quantifying Entanglement
• Decoherence Free Subspaces for Quantum Computation
• Quantum metrology with nonclassical states of atomic ensembles
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Many-particle entanglement with Bose--Einstein condensates
• Multidimensional quantum entanglement with large-scale integrated optics
• Efficient quantum state tomography
• Entanglement and Extreme Spin Squeezing
• Characterizing Entanglement
• Experimental entanglement of a six-photon symmetric Dicke state
• Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in a Bose-Einstein condensate
• Permutationally invariant quantum tomography
• Measurements in two bases are sufficient for certifying high-dimensional entanglement
• Spatially distributed multipartite entanglement enables Einstein-Podolsky-Rosen steering of atomic clouds
• Entanglement between two spatially separated atomic modes
• Sample-optimal tomography of quantum states
• Systematic errors in current quantum state tomography tools
• Linking a distance measure of entanglement to its convex roof
• Bell inequalities tailored to maximally entangled states
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
• Error Estimation for Moments Analysis in Heavy-Ion Collision Experiments
• Scalable on-chip quantum state tomography
• Practical adaptive quantum tomography
• Optimal witnessing of the quantum Fisher information with few measurements
• Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
• Adaptive quantum tomography
• Bell inequalities tailored to the Greenberger-Horne-Zeilinger states of arbitrary local dimension
• Efficient quantum tomography
• Efficient quantum tomography II

Cited by in corpus (5)

• Entanglement quantification in atomic ensembles
• Machine Learning Universal Bosonic Functionals
• The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
• Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach
• Symmetric quantum states: a review of recent progress