Probing post-measurement entanglement without post-selection

Abstract

We study the problem of observing quantum collective phenomena emerging from large numbers of measurements. These phenomena are difficult to observe in conventional experiments because, in order to distinguish the effects of measurement from dephasing, it is necessary to post-select on sets of measurement outcomes whose Born probabilities are exponentially small in the number of measurements performed. An unconventional approach, which avoids this exponential `post-selection problem', is to construct cross-correlations between experimental data and the results of simulations on classical computers. However, these cross-correlations generally have no definite relation to physical quantities. We first show how to incorporate shadow tomography into this framework, thereby allowing for the construction of quantum information-theoretic cross-correlations. We then identify cross-correlations which both upper and lower bound the measurement-averaged von Neumann entanglement entropy, and additional cross-correlations which lower bound the measurement-averaged purity and entanglement negativity. These bounds show that experiments can be performed to constrain post-measurement entanglement without the need for post-selection. To illustrate our technique we consider how it could be used to observe the measurement-induced entanglement transition in Haar-random quantum circuits. We use exact numerical calculations as proxies for quantum simulations and, to highlight the fundamental limitations of classical memory, we construct cross-correlations with tensor-network calculations at finite bond dimension. Our results reveal a signature of measurement-induced criticality that can be observed using a quantum simulator in polynomial time and with polynomial classical memory.

13 pages

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Cited by in corpus (38)

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• Entanglement Transition due to particle losses in a monitored fermionic chain
• Monitored long-range interacting systems: spin-wave theory for quantum trajectories
• Dynamics of Pseudoentanglement
• Efficient Local Classical Shadow Tomography with Number Conservation
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Entanglement swapping in critical quantum spin chains
• Protect Measurement-Induced Phase Transition from Noise
• Entanglement transitions induced by quantum-data collection
• Local and nonlocal stochastic control of quantum chaos: Measurement- and control-induced criticality
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Boundary transitions from a single round of measurements on gapless quantum states
• Measurement-induced phase transitions in systems with diffusive dynamics
• Observable-projected ensembles
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Hardness of observing strong-to-weak symmetry breaking
• Matchgate circuits deeply thermalize
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Variational post-selection for ground states and thermal states simulation
• Random Quantum Circuits with Time-Reversal Symmetry
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Observable Measurement-Induced Transitions
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Violation of steering inequality for generalized equiangular measurements
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information
• Deterministic quantum trajectory via imaginary time evolution
• Post-measurement Quantum Monte Carlo
• Artificial intelligence for representing and characterizing quantum systems
• Noisy Monitored Quantum Circuits
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems