Visualizing Two Qubits

Abstract

The notions of entanglement witnesses, separable and entangled states for two qubits system can be visualized in three dimensions using the SLOCC equivalence classes. This visualization preserves the duality relations between the various sets and allows us to give ``proof by inspection'' of a non-elementary result of the Horodeckies that for two qubits, Peres separability test is iff. We then show that the CHSH Bell inequalities can be visualized as circles and cylinders in the same diagram. This allows us to give a geometric proof of yet another result of the Horodeckies, which optimizes the violation of the CHSH Bell inequality. Finally, we give numerical evidence that, remarkably, allowing Alice and Bob to use three rather than two measurements each, does not help them to distinguish any new entangled SLOCC equivalence class beyond the CHSH class.

22 pages, 5 figures. Added several references

References in corpus (13)

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• Bell Inequalities and the Separability Criterion
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Cited by in corpus (11)

• Quantum Steering Ellipsoids
• Quantum steering ellipsoids, extremal physical states and monogamy
• Entanglement and the geometry of two qubits
• A Concise Formula for Generalized Two-Qubit Hilbert-Schmidt Separability Probabilities
• Canonical forms of two-qubit states under local operations
• Geometric representation of two-qubit entanglement witnesses
• The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group SL(3,C)
• Extended Studies of Separability Functions and Probabilities and the Relevance of Dyson Indices
• Quantum Zermelo problem for general energy resource bounds
• Generalized Two-Qubit Whole and Half Hilbert-Schmidt Separability Probabilities
• Lorentz canoncial forms of two-qubit states