), are referred to as post-measurement states. The above has shown that any 2-qubit state can actually be decomposed into a variety of possible superposition of 2-qubit pairs, as selected from the family {100), |01), |10), |11)}. Of particular interest is the specific subgroup of 2-qubit pair superpositions |ij) + |kl), where i # k or j #1, conventionally defined according to: 1000)= (16.12) The family of 2-qubit superpositions defined in the above inventory is referred to as Bell states or EPR pairs, the EPR acronym being short for the names Einstein, Podolsky, and Rosen. The Bell or EPR states exhibit quite intriguing and useful properties for quantum computing, as will be described in Chapter 18. The key lesson we have learnt SO far is that, unlike classical bits, qubits are not physically observable. But, as I shall describe next, qubits can be physically manipu- lated! Such a manipulation, which transforms the qubit state, is of consequence in the measurable or experimental domain. Hence, we may conceive of a quantum computer, a machine that processes information not from bits but from qubits. The fact that qubits are a probabilistic superposition of states introduces new dimensions and perspectives in computing power, which represents a key justification for QIT. Basic computations with 1-qubit quantum gates In Chapter 15, we have described the principles of reversible-logic gates, as based on classical bit inputs and controls. Here, we shall explore how such gates can perform 16.2 Basic computations with 1-qubit quantum gates elementary computations by exclusive use of qubits, instead of classical bits. As we will discover, quantum computation based on these two principles is quite different in nature and in power, when compared with classical computation obtained from mere Boolean-logic gates. We shall first consider operations with single qubit states, and then move to more complex ones involving two and three qubit states. As we have seen earlier in this chapter, a single qubit (or 1-qubit), /q), is def