Quantum mechanics violates everyday intuition not only because the measured data can only be predicted probabilistically but also because of a quantum-specific correlation called entanglement. It is believed that this type of correlation does not exist in macroscopic objects. Entanglement can be used to cause nonlocal phenomena. States possessing such correlations are called entangled states (or states that possess entanglement). Among these states, the states with the highest degree of entanglement are called maximally entangled states or EPR states. Historically, the idea of a nonlocal effect due to entanglement was pointed out by Einstein, Podolsky, and Rosen; hence, the name EPR state.
In order to transport a quantum state over a long distance, we have to retain its coherence during its transmission. However, it is often very difficult because the transmitted system can be easily correlated with the environment system. If the sender and receiver share an entangled state, the sender can transport his/her quantum state to the receiver without transmitting it, as is mentioned in Chap. 9. This protocol is called quantum teleportation and clearly explains the effect of entanglement in quantum systems. Many other effects of entanglement have also been examined, some of which are given in Chap. 9.
However, it is difficult to take advantage of entanglement if the shared state is insufficiently entangled. Therefore, one topic of investigation will be to discuss how much of a maximally entangled state can be extracted from a state with a small amount of entanglement. Of course, if we allow quantum operations between two systems, we can always produce maximally entangled states. Therefore, we examine cases where only local quantum operations and classical communications are allowed.
KeywordsEntangle State Pure State Locality Restriction Classical Communication Positive Partial Transpose
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