Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems

Abstract

We present a set of inequalities for detecting quantum entanglement of $2\otimes d$ quantum states. For $2\otimes 2$ and $2\otimes 3$ systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of $d>3$, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of $2\otimes d$ quantum states and even multi-qubit pure states.

6 pages

References in corpus (8)

• Concurrence of arbitrary dimensional bipartite quantum states
• Efficient Toffoli Gates Using Qudits
• Lower bounds on concurrence and separability conditions
• Separability criteria and bounds for entanglement measures
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Majorization criterion for distillability of a bipartite quantum state
• Entanglement sudden death in qubit-qutrit systems
• Lower Bounds of Concurrence for Tripartite Quantum Systems