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Can Quantum entanglement can be used to strengthen the security or increase the efficiency of communication via the BB84 protocol? If so, how?

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All different QKD protocols are well covered in most Quantum Information textbooks, e.g. Quantum Information by Jaeger. Trying to give a complete, understandable coverage of the matter is impossible in a post like this, so I'll just give you an overview:

In the E91 scheme, entangled photon pairs are used between Alice & Bob, and unlike the single-photon measurements performed in BB84, here Bell states are used. The first direct consequence of using entangled qubits, is the provision of fully randoms bits to both parties where the bits are correlated with each other(ideally with maximally entangled two-qubit states.)

Unlike BB84, Alice does not provide the prepared qubits, instead a distributor is used, which creates entangled-pairs, and sends each one of them to both Alice and Bob. They perform their measurement using their sets of basis (2-3 different bases). Here also the choice of basis is usual done randomly and all their measurements performed independently. Then they retain only the bits obtained from measurements using the same basis, because knowing they're using entangled-pairs, their results would be perfectly correlated.

Finally bear in mind that the biggest difference here is the fact that Eve will not be able to detect qubit states without inducing errors in the corresponding subspace, whereas in the usual single photon BB84 Eve has the possibility (with a certain probability of course) to measure bits without changing their states, had she luckily chosen the same basis as Alice had used to prepare the qubit's polarization. All in all, this protocol makes Eve's influence more easily "noticeable" due to the nature of the E91 protocol.

To sum up, this was only a crude overview, the protocol has as many nuances as the famous BB84 does, even more, and to able to say whether E91 is more efficient or not is rather difficult without a full understanding of both, or without specific scenarios in mind. Just keep in mind that the main idea is to have fully random shared-key established between Alice and Bob, without any of its bits having been leaked in the process. In this regard E91 may provide a more secure establishment using entangled qubit pairs, and their encryption methods/algorithms remain among the existing classical ones.

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