Disentangling Theorem and Monogamy for Entanglement Negativity

Abstract

Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave-function of three subsystems $A$, $B$, and $C$ factorizes into a product state for parts $A{B}_1$ and $B_{2}C$; and a monogamy relation, which states that if $A$ is very entangled with $B$, then $A$ cannot be simultaneaously very entangled also with $C$.

6 pages, 2 figures

References in corpus (9)

• Entanglement negativity in quantum field theory
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• General monogamy relation for the entanglement of formation in multiqubit systems
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Entanglement negativity via replica trick: a Quantum Monte Carlo approach

Cited by in corpus (47)

• General Monogamy of Tsallis $q$-Entropy Entanglement in Multiqubit Systems
• Tighter monogamy relations in multipartite systems
• Analytical characterization of the genuine multiparticle negativity
• Monogamy of entanglement without inequalities
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Multipartite Entanglement Measure and Complete Monogamy Relation
• Monogamy of the Entanglement of Formation
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Entanglement structures in qubit systems
• Independence of work and entropy for equal energetic finite quantum systems: Passive state energy as an entanglement quantifier
• Finer Distribution of Quantum Correlations among Multiqubit Systems
• On Strong Monogamy Conjecture in Four-Qubit System
• Conditions for monogamy of quantum correlations in multipartite systems
• Deterministic Quantum Dense Coding Networks
• Monogamy of quantum entanglement
• Monogamy of entanglement for tripartite systems
• Bounding entanglement wedge cross sections
• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Universality in Distribution of Monogamy Scores for Random Multiqubit Pure States
• Monogamy properties of qubit systems
• Complete monogamy of the multipartite quantum mutual information
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Quantum Circuit Model of Black Hole Evaporation
• Faithful geometric measures for genuine tripartite entanglement
• Generalized monogamy inequalities of convex-roof extended negativity in $N$-qubit systems
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Monogamy and polygamy relations of quantum correlations for multipartite systems
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Activation of Nonmonogamous Multipartite Quantum States
• General Monogamy and polygamy properties of quantum systems
• Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy
• Complete Genuine Multipartite Entanglement Monotone
• Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
• Restrictions on shareability of classical correlations for random multipartite quantum states
• Tighter monogamy relations of entanglement measures based on fidelity
• On Monogamy of four qubit entanglement
• Monogamy Relations for Multiqubit Systems
• Emergence of Monogamy under Static and Dynamic Scenarios
• Multipartite Monogamy of Entanglement for Three Qubit States
• Entanglement and firewalls in quantum circuit model of black hole evaporation
• Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions
• General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems
• Monogamous nature of symmetric multiqubt states with distinct spinors