Estimating localizable entanglement from witnesses
arXiv:1803.02753 · doi:10.1088/1367-2630/aac485
Abstract
Computing localizable entanglement for noisy many-particle quantum states is difficult due to the optimization over all possible sets of local projection measurements. Therefore, it is crucial to develop lower bounds, which can provide useful information about the behaviour of localizable entanglement, and which can be determined by measuring a limited number of operators, or by performing least number of measurements on the state, preferably without performing a full state tomography. In this paper, we adopt two different yet related approaches to obtain a witness-based, and a measurement-based lower bounds for localizable entanglement. The former is determined by the minimal amount of entanglement that can be present in a subsystem of the multipartite quantum state, which is consistent with the expectation value of an entanglement witness. Determining this bound does not require any information about the state beyond the expectation value of the witness operator, which renders this approach highly practical in experiments. The latter bound of localizable entanglement is computed by restricting the local projection measurements over the qubits outside the subsystem of interest to a suitably chosen basis. We discuss the behaviour of both lower bounds against local physical noise on the qubits, and discuss their dependence on noise strength and system size. We also analytically determine the measurement-based lower bound in the case of graph states under local uncorrelated Pauli noise.
arXiv comment19 pages, 7 figures
References in corpus (71)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Many-Body Physics with Ultracold Gases
- Experimental quantum teleportation
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Introducing Quantum Discord
- Entanglement of a Pair of Quantum Bits
- Distributed Entanglement
- Topological entanglement entropy
- Entanglement detection
- Classical, quantum and total correlations
- Scaling of Entanglement close to a Quantum Phase Transitions
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Measurement-based quantum computation with cluster states
- The logarithmic negativity: A full entanglement monotone that is not convex
- Entanglement in a simple quantum phase transition
- Entanglement spectrum of a topological phase in one dimension
- Measurement-based quantum computation
- Quantum Cryptography with Entangled Photons
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms
- Quantum entanglement in photosynthetic light harvesting complexes
- Identifying Topological Order by Entanglement Entropy
- Witnessing multipartite entanglement
- Entanglement versus Correlations in Spin Systems
- Measures and dynamics of entangled states
- Diverging Entanglement Length in Gapped Quantum Spin Systems
- Graphical description of the action of local Clifford transformations on graph states
- Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
- Computing quantum discord is NP-complete
- Detection of entanglement with few local measurements
- Entanglement Detection in the Stabilizer Formalism
- Entanglement Percolation in Quantum Networks
- Concurrence of mixed bipartite quantum states in arbitrary dimensions
- Localizable Entanglement
- Quantifying Entanglement with Witness Operators
- Concurrence of mixed multi-partite quantum states
- Quantitative entanglement witnesses
- Partial Teleportation of Entanglement in the Noisy Environment
- Benchmarking quantum control methods on a 12-qubit system
- Long-range quantum entanglement in noisy cluster states
- Quantum channels and their entropic characteristics
- Estimating entanglement measures in experiments
- Statistical mechanics of the Cluster-Ising model
- The AdS/CFT Correspondence
- Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
- Phase diagram and quench dynamics of the Cluster-XY spin chain
- Open-system dynamics of graph-state entanglement
- Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
- Entanglement flow in multipartite systems
- Multipartite Quantum Entanglement Evolution in Photosynthetic Complexes
- Lower bounds on entanglement measures from incomplete information
- Witnessed Entanglement
- Noisy entanglement evolution for graph states
- Entanglement criteria and full separability of multi-qubit quantum states
- Multipartite Entanglement Accumulation in Quantum States: Localizable Generalized Geometric Measure
- Optimal Detection of Entanglement in GHZ States
- Concurrence of quasi pure quantum states
- Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits
- Quantum Computation with Topological Codes: from qubit to topological fault-tolerance
- Macroscopic bound entanglement in thermal graph states
- Arboreal Bound Entanglement
- Entanglement in pure and thermal cluster states
- Reducing Computational Complexity of Quantum Correlations
- Mapping the spatial distribution of entanglement in optical lattices
- Highly-efficient estimation of entanglement measures for large experimentally created graph states via simple measurements
Cited by in corpus (14)
- The controlled SWAP test for determining quantum entanglement
- Design and Experimental Performance of Local Entanglement Witness Operators
- Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits
- Uniform Decoherence Effect on Localizable Entanglement in Random Multi-qubit Pure States
- Scalable characterization of localizable entanglement in noisy topological quantum codes
- Resource theoretic efficacy of the single copy of a two-qubit entangled state in a sequential network
- Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field
- Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
- Localizing genuine multiparty entanglement in noisy stabilizer states
- Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
- Localizing multipartite entanglement with local and global measurements
- Emergence of Monogamy under Static and Dynamic Scenarios
- Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
- Recovery of resources through sequential noisy measurements