Geometry of quantum state space and quantum correlations

Abstract

Quantum state space is endowed with a metric structure and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by 2x2 density matrices, we determine a particular Riemannian metric for a state \r{ho} and show that if \r{ho} gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equals to square root of that particular Riemannian metric . Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.

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References in corpus (5)

• Measuring Quantum Coherence with Entanglement
• Observable measure of quantum coherence in finite dimensional systems
• Quantum information can be negative
• Geometric lower bound for a quantum coherence measure
• Partial transpose as a direct link between concurrence and negativity

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• Genuine quantum coherence
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• Geometry of quantum state space and entanglement
• Reproducing kernel Hilbert C*-module and kernel mean embeddings
• Kernel Mean Embeddings of Von Neumann-Algebra-Valued Measures