W States
W states are multi-qubit entangled states whose entanglement survives the loss of a qubit, unlike the fragile GHZ states.
A robust kind of entanglement
The W state is a class of multi-qubit entangled state distinct from the GHZ state. For three qubits it is (|100> + |010> + |001>)/sqrt(3): exactly one qubit is excited, in an equal superposition over which one. It represents a fundamentally different pattern of entanglement.
Two inequivalent classes
For three qubits there are two classes of genuine tripartite entanglement that cannot be converted into each other by local operations: the GHZ class and the W class. This is a striking fact — multipartite entanglement is not one thing but several inequivalent kinds, and W states are the canonical representative of the second class.
Robustness to loss
The defining virtue of the W state is robustness. If you lose or measure one qubit of a three-qubit W state, the remaining two are still entangled. Contrast this with the GHZ state, where losing one qubit leaves the rest in an unentangled mixture. W-state entanglement is distributed more resiliently across the parties.
- GHZ: maximal correlation, but destroyed by loss of any one qubit
- W: less maximal, but entanglement persists under particle loss
- The two cannot be interconverted by local operations and classical communication
Preparation
W states are somewhat harder to prepare than GHZ states, requiring a sequence of controlled rotations that distribute a single excitation across the qubits in the right superposition. They do not arise from the simple Hadamard-plus-CNOT-chain that makes GHZ states.
Where they are used
The persistence of W-state entanglement makes it attractive for tasks needing fault tolerance against qubit loss, such as certain quantum memory and communication schemes, and leader-election protocols. As a benchmark, preparing and verifying a high-fidelity W state tests a processor's ability to create a genuinely different entanglement structure than the more common GHZ.