Quantum criticality under imperfect teleportation

Abstract

Entanglement, measurement, and classical communication together enable teleportation of quantum states between distant parties, in principle with perfect fidelity. To what extent do correlations and entanglement of a many-body wavefunction transfer under imperfect teleportation protocols? We address this question for the case of an imperfectly teleported quantum critical wavefunction, focusing on the ground state of a critical Ising chain. We demonstrate that imperfections, e.g., in the entangling gate adopted for a given protocol, effectively manifest as weak measurements acting on the otherwise pristinely teleported critical state. Armed with this perspective, we leverage and further develop the theory of measurement-altered quantum criticality to quantify the resilience of critical-state teleportation. We identify classes of teleportation protocols for which imperfection $(i)$ preserves both the universal long-range entanglement and correlations of the original quantum critical state, $(ii)$ weakly modifies these quantities away from their universal values, and $(iii)$ obliterates long-range entanglement altogether while preserving power-law correlations, albeit with a new set of exponents. We also show that mixed states describing the average over a series of sequential imperfect teleportation events retain pristine power-law correlations due to a `built-in' decoding algorithm, though their entanglement structure measured by the negativity depends on errors similarly to individual protocol runs. These results may allow one to design teleportation protocols that optimize against errors -- highlighting a potential practical application of measurement-altered criticality.

25 pages, 10 figures. Published version

References in corpus (57)

• Experimental quantum teleportation
• A computable measure of entanglement
• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• An Area Law for One Dimensional Quantum Systems
• Ground-to-satellite quantum teleportation
• Advances in Quantum Teleportation
• Reduced density matrices and entanglement entropy in free lattice models
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Measurement-driven entanglement transition in hybrid quantum circuits
• Unitary-projective entanglement dynamics
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Entanglement in a fermion chain under continuous monitoring
• Entanglement negativity in extended systems: A field theoretical approach
• Entanglement entropy for the long range Ising chain
• Long distance quantum teleportation in a quantum relay configuration
• Quantum teleportation on a photonic chip
• Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
• Quantum criticality under decoherence or weak measurement
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Measurement as a shortcut to long-range entangled quantum matter
• Ordering in spatially anisotropic triangular antiferromagnets
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Measurement-induced dynamics of many-body systems at quantum criticality
• Long-range entanglement from measuring symmetry-protected topological phases
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Wave Function and Strange Correlator of Short Range Entangled states
• Unitarity of black hole evaporation in final-state projection models
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Measurements conspire nonlocally to restructure critical quantum states
• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
• Solution of the fermionic entanglement problem with interface defects
• Order parameter statistics in the critical quantum Ising chain
• Teleportation of entanglement over 143 km
• Mixed-state long-range order and criticality from measurement and feedback
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
• Area law of non-critical ground states in 1D long-range interacting systems
• Entanglement entropy in the Long-Range Kitaev chain
• Entanglement in one-dimensional critical state after measurements
• Measurement-altered Ising quantum criticality
• Probing sign structure using measurement-induced entanglement
• Channeling quantum criticality
• Nonlocality and entanglement in measured critical quantum Ising chains
• Magnetization distribution in the transverse Ising chain with energy flux
• Measurement-induced phase transitions on dynamical quantum trees
• Correlations at PT-symmetric quantum critical point
• Shadow tomography from emergent state designs in analog quantum simulators
• Measurements on an Anderson Chain
• Evolution of many-body systems under ancilla quantum measurements
• Postselection-free learning of measurement-induced quantum dynamics
• Ultrafast Entanglement Dynamics in Monitored Quantum Circuits
• Steering-induced phase transition in measurement-only quantum circuits
• Holographic Weak Measurement
• Spin correlation function in 2D statistical mechanics models with inhomogeneous line defects

Cited by in corpus (10)

• Robust teleportation of a surface code and cascade of topological quantum phase transitions
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Stabilizer Rényi Entropy and Conformal Field Theory
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Boundary transitions from a single round of measurements on gapless quantum states
• Quantum teleportation implies symmetry-protected topological order
• Dissipation meets conformal interface in open quantum systems: How the relaxation rate is suppressed
• Post-measurement Quantum Monte Carlo
• Unitary and non-unitary operators leverage perfect and imperfect single qutrit teleportation
• Quality assessment of quantum teleportation through the distribution of fidelity