The most strikingly quantum-mechanical situations phenomena involve entangled states with components located in spacelike-separated regions, customarily referred to as laboratories. Each laboratory is taken to contain a physical agent capable of performing quantum operations on subsystems within it and potentially communicating with agents in other laboratories, via either oneway or two-way classical and quantum communication channels. When considering two-component systems described by bipartite statistical operators, ρAB, the corresponding two agents are customarily referred to as “Alice” and “Bob,” with the labels A and B indicating the corresponding subsystems or laboratories. Entanglement-based quantum-key-distribution systems are practical examples in which this convention accurately reflects the experimental situation. Locality considerations are often explicitly brought into play when studying entanglement. However, it should also be kept in mind that it is by no means obvious that violations of locality conditions in the traditional sense are sufficient for the characterization of entanglement, despite their value in the investigation of entangled quantum states. The distinction between locality violation and quantum state entanglement should therefore be kept in mind. This chapter focuses on entanglement more in relation to local operations themselves than in relation to information, which relation is the focus of Chapter 6; the intervening chapters introduce various information-theoretic concepts and quantities, both classical and quantum, that will prove essential for the important and often subtle discussion taken up there.
KeywordsQuantum Circuit Bell Inequality Quantum Nonlocality Interference Visibility CHSH Inequality
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