Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures

Abstract

Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to quantify entanglement and coherence based on the full information of the experimentally realized multipartite states. Fortunately, other methods have been found to directly measure the fidelity of experimental states without quantum state tomography. Here we present a fidelity-based method to derive experimentally accessible lower bounds for measures of genuine multipartite entanglement and coherence. On the one hand, the method works for genuine multipartite entanglement measures including the convex-roof extended negativity, the concurrence, the G-concurrence, and the geometric measure for genuine multipartite entanglement. On the other hand, the method also delivers observable lower bounds for the convex roof of the $l_1$-norm of coherence, the geometric measure of coherence, and the coherence of formation. Furthermore, all the lower bounds are based on the fidelity between the chosen pure state and the target state, and we obtain the lower bounds of several real experimental states as examples of our results.

arXiv comment10 pages, 4 figures

References in corpus (64)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• 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
• Three qubits can be entangled in two inequivalent ways
• Entanglement of a Pair of Quantum Bits
• Quantifying Coherence
• Entanglement detection
• Quantum Coherence as a Resource
• On the volume of the set of mixed entangled states
• Quantum Resource Theories
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• Universal state inversion and concurrence in arbitrary dimensions
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Four qubits can be entangled in nine different ways
• Robustness of coherence: An operational and observable measure of quantum coherence
• Classification of mixed three-qubit states
• Experimental ten-photon entanglement
• Witnessing multipartite entanglement
• Entanglement Measures under Symmetry
• Characterizing Entanglement
• Observation of eight-photon entanglement
• Intrinsic randomness as a measure of quantum coherence
• Separability criteria for genuine multiparticle entanglement
• Measure of genuine multipartite entanglement with computable lower bounds
• Quantum coherence and geometric quantum discord
• Computing quantum discord is NP-complete
• Separability and distillability of multiparticle quantum systems
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Concurrence of mixed bipartite quantum states in arbitrary dimensions
• The Entanglement of Formation for Isotropic States
• Monotones and invariants for multi-particle quantum states
• Quantitative entanglement witnesses
• I-concurrence and tangle for isotropic states
• Genuine 12-qubit entanglement on a superconducting quantum processor
• The structure of multidimensional entanglement in multipartite systems
• Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
• Estimating entanglement measures in experiments
• Variational Characterisations of Separability and Entanglement of Formation
• General monogamy relation for the entanglement of formation in multiqubit systems
• Detecting genuine multipartite quantum non-locality -- a simple approach and generalization to arbitrary dimension
• Measuring Coherence with Entanglement Concurrence
• Family of Concurrence Monotones and its Applications
• Nonlinear entanglement witnesses
• Multipartite entanglement detection from correlation tensors
• When are correlations quantum? -- Verification and quantification of entanglement by simple measurements
• Witnessing genuine multipartite entanglement with positive maps
• The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
• Entanglement criteria for Dicke states
• Roofs and Convexity
• Analytical characterization of the genuine multiparticle negativity
• Quantify entanglement by concurrence hierarchy
• Concurrence in arbitrary dimensions
• Estimating entanglement monotones with a generalization of the Wootters formula
• Axiomatic and operational connections between the $l_1$-norm of coherence and negativity
• Measures of entanglement in multipartite bound entangled states
• Detecting and estimating continuous-variable entanglement by local orthogonal observables
• Detecting coherence via spectrum estimation
• Evaluating the geometric measure of multiparticle entanglement
• Tight Bounds for the Entanglement of Formation of Gaussian States
• Evaluation of entanglement measures by a single observable

Cited by in corpus (25)

• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure
• Geometry of faithful entanglement
• Maximal steered coherence and its conversion to entanglement in multiple bosonic reservoirs
• Quantum Error Mitigated Classical Shadows
• Detecting and estimating coherence based on coherence witnesses
• Experimentally accessible bounds on distillable entanglement from entropic uncertainty relations
• Detecting genuine multipartite entanglement via machine learning
• Efficient estimation of multipartite quantum coherence
• Analyzing quantum entanglement with the Schmidt decomposition in operator space
• Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement
• Multipartite entanglement detection based on generalized state-dependent entropic uncertainty relation for multiple measurements
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• Factorization dynamics between quantum Fisher information and quantum coherence
• Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states
• A generic framework for genuine multipartite entanglement detection
• Lower bounds on concurrence and negativity from a trace inequality
• Experimental Entanglement Quantification for Unknown Quantum States in a Semi-Device-Independent Manner
• Detecting coherence with respect to general quantum measurements
• Tensor Rank and Other Multipartite Entanglement Measures of Graph States
• Interconversion between block coherence and multipartite entanglement in many-body systems
• The tightness of multipartite coherence from spectrum estimation
• Localizing multipartite entanglement with local and global measurements
• Classifying coherence with a finite set of witnesses
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement