Invariant-based entanglement monotones as expectation values and their experimental detection

Abstract

Characterization and quantification of multipartite entanglement is one of the challenges in state-of-the-art experiments in quantum information processing. According to theory, this is achieved via entanglement monotones, that is, functions that do not increase under stochastic local operations and classical communication (SLOCC). Typically such monotones include the wave function and its time-reversal (antilinear-operator formalism) or they are based on not completely positive maps (e.g., partial transpose). Therefore, they are not directly accessible to experimental observations. We show how entanglement monotones derived from polynomial local SL$(2,\CC)$ invariants can be re-written in terms of expectation values of observables. Consequently, the amount of entanglement---of specific SLOCC classes---in a given state can be extracted from the measurement of correlation functions of local operators.

6 pages, revtex4-1. An erroneous formula has been repaired. Several concepts are explained better. Updated references. To be published in Phys. Rev. A

References in corpus (19)

• Entanglement detection
• 14-qubit entanglement: creation and coherence
• Observation of eight-photon entanglement
• Experimental demonstration of topological error correction
• Constructing N-qubit entanglement monotones from anti-linear operators
• Entangled three-qubit states without concurrence and three-tangle
• Estimating entanglement measures in experiments
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• On experimental procedures for entanglement verification
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• On polynomial invariants of several qubits
• Tangles of superpositions and the convex-roof extension
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• Measurable entanglement for tripartite quantum pure states of qubits
• Multipartite-entanglement monotones and polynomial invariants
• Estimating multipartite entanglement measures
• Quantifying mixed-state quantum entanglement by optimal entanglement witness
• Can measuring entanglement be easy?

Cited by in corpus (15)

• Quantifying entanglement resources
• Evaluation of convex roof entanglement measures
• Almost all multipartite qubit quantum states have trivial stabilizer
• Symmetry criteria for quantum simulability of effective interactions
• Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
• Entanglement of four qubit systems: a geometric atlas with polynomial compass I (the finite world)
• Collectibility for Mixed Quantum States
• Parametrization and optimization of Gaussian non-Markovian unravelings for open quantum dynamics
• Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)
• Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication
• Constructive entanglement test from triangle inequality
• The Entanglement Hierarchy 2 x m x n Systems
• Two methods for measuring Bell nonlocality via local unitary invariants of two-qubit systems in Hong-Ou-Mandel interferometers
• Classification of multipartite systems featuring only $|W⟩$ and $|GHZ⟩$ genuine entangled states