# Understanding Bennett's laws for quantum information

Charles Bennett's laws of quantum information are (see https://en.wikipedia.org/wiki/Bennett%27s_laws):

1. 1 qubit $$\succeq$$ 1 bit
2. 1 qubit $$\succeq$$ 1 ebit
3. 1 ebit + 1 qubit $$\succeq$$ 2 bits
4. 1 ebit + 2 bits $$\succeq$$ 1 qubit.

As explained in Schumacher and Westmoreland's book on quantum theory ("Quantum Processes, Systems, and Information"), these laws are to be understood in the context of a standard "Alice and Bob" situation, where we suppose that Alice and Bob each have separate laboratories in which they can perform any local unitary operations and local measurements on the quantum systems in their possession. In addition:

• "1 bit" means that Alice can send an ordinary one-bit message to Bob, or vice versa.
• "1 qubit" means that Alice can transfer a qubit quantum systom to Bob, or vice versa.
• "1 ebit" (entanglement bit) means that Alice and Bob share an entangled qubit pair in a Bell state (or some equivalent state).

The symbol $$\succeq$$ means, according to Schumacher and Westmoreland, that the resources on the left hand side "can be used to do any task that can be performed" using the resources on the right hand side. The Wikipedia article simply defines the symbol $$\succeq$$ to mean "can do the job of".

Now, the first law makes perfectly sense to me, as Alice can encode a classical bit of information in the basis states of a qubit, then tranfer the qubit to Bob, who can then recover the message by measuring the qubit in Alice's basis. All this seems to require, is that Alice and Bob have agreed on a code in advance.

However, I'm not sure I understand the second law. Is the point simply that Alice, in the privacy of her local lab, can prepare a pair of qubits in an entangled Bell state, and then send one of the qubits to Bob? Now they share an ebit. Is it that simple?