may be and even though both can not tell if their qubit has value “0” or “1” — a most surprising circumstance that can not be explained by classical physics. Controlled gate to construct the Bell state Controlled gates act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the controlled NOT gate (or CNOT or CX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is , and otherwise leaves it unchanged. With respect to the unentangled product basis , , , , it maps the basis states as follows: . A common application of the CNOT gate is to maximally entangle two qubits into the Bell state. To construct , the inputs A (control) and B (target) to the CNOT gate are: and After applying CNOT, the output is the Bell State: . Applications The Bell state forms part of the setup of the superdense coding, quantum teleportation, and entangled quantum cryptography algorithms. Quantum entanglement also allows multiple states (such as the Bell state mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation. A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of quantum circuits that can be executed reliably. Quantum register A number of qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. Qudits and qutrits The term qudit denotes the unit of quantum information that can be realized in suitable d-level quantum systems. A qubit register that can be measured to N states is identical to an N-level qudit. A rarely used synonym for qudit is quNit, since both d and N are frequently used to denote the dimension of a quantum system. Qudits are similar to the integer types in classical computing, and may be mapped to (or realized by) arrays of qubits. Qudits where the d-level system is not