Anisotropic invariance and the distribution of quantum correlations
arXiv:1610.09302 · doi:10.1103/PhysRevLett.118.010401
Abstract
We report the discovery of two new invariants for three-qubit states which, similarly to the 3-tangle, are invariant under local unitary transformations and permutations of the parties. These quantities have a direct interpretation in terms of the anisotropy of pairwise spin correlations. Applications include a universal ordering of pairwise quantum correlation measures for pure three-qubit states; tradeoff relations for anisotropy, 3-tangle and Bell nonlocality; strong monogamy relations for Bell inequalities, Einstein-Podolsky-Rosen steering inequalities, geometric discord and fidelity of remote state preparation (including results for arbitrary three-party states); and a statistical and reference-frame-independent form of quantum secret sharing.
arXiv comment5+5 pages, close to published version and minor clarifications to Supplementary Material in page S4
References in corpus (30)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Three qubits can be entangled in two inequivalent ways
- Quantum secret sharing
- Entanglement of a Pair of Quantum Bits
- Bell nonlocality
- Distributed Entanglement
- The classical-quantum boundary for correlations: discord and related measures
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Necessary and sufficient condition for non-zero quantum discord
- Remote State Preparation
- Minimum cbits for remote preperation and measurement of a qubit
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- Generalized Schmidt decomposition and classification of three-quantum-bit states
- Quantum discord as resource for remote state preparation
- Quantum Communication between N partners and Bell's inequalities
- Quantification of Einstein-Podolski-Rosen steering for two-qubit states
- Are general quantum correlations monogamous?
- Three-qubit pure-state canonical forms
- Monogamy inequalities for the EPR paradox and quantum steering
- One-qubit reduced states of a pure many-qubit state: polygon inequalities
- Analog of the Clauser-Horne-Shimony-Holt inequality for steering
- Quantum Key Distribution between N partners: optimal eavesdropping and Bell's inequalities
- Volume monogamy of quantum steering ellipsoids for multi-qubit systems
- All two-qubit states that are steerable via Clauser-Horne-Shimony-Holt-type correlations are Bell nonlocal
- Trade-off Relations of Bell Violations among Pairwise Qubit Systems
- Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States
- Necessary and sufficient conditions for multipartite Bell violations with only one trusted device
- Distribution of Bell inequality violation vs. multiparty quantum correlation measures
- Simple permutation-based measure of quantum correlations and maximally-3-tangled states
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- Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
- Quantum discord and its allies: a review
- Monogamy of entanglement without inequalities
- Continuous variables triple-photon states quantum entanglement
- Multipartite Entanglement Measure and Complete Monogamy Relation
- Monogamy of the Entanglement of Formation
- Entanglement of three-qubit random pure states
- Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering
- Shareability of Quantum Steering and its Relation with Entanglement
- Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states
- Tripartite entanglement measure under local operations and classical communication
- Any entanglement of assistance is polygamous
- When is a Genuine Multipartite Entanglement Measure Monogamous?
- Hidden Non n-locality In Linear Networks
- Shareability of steering in 2-producible states
- Information-disturbance trade-off in generalized entanglement swapping
- Correlation constraints and the Bloch geometry of two qubits
- Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
- Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
- Trade-off relations of l_1-norm coherence for multipartite systems
- Monogamy relations for nonclassical correlations of multi-qubit states
- Tsallis entropy, -expectation and constraints on three-party quantum correlations
- Characterizing nonlocality of pure symmetric three-qubit states
- Experimental Verification of Anisotropic Invariance for Three-Qubit States
- Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems
- Distribution of spin correlation strengths in multipartite systems
- Geometry of two-body correlations in three-qubit states
- Trade-off relations on CHSH tests for multi-qubit pure states
- Probe of Generic Quantum Contextuality and Nonlocal Resources for Qubits
- Robust Multipartite Entanglement Without Entanglement Breaking