W state
The W state is an
and which is remarkable for representing a specific type of
Properties
The W state is the representative of one of the two non-biseparable[3] classes of three-qubit states, the other being the Greenberger–Horne–Zeilinger state, , which cannot be transformed (not even probabilistically) into each other by local quantum operations.[2] Thus and represent two very different kinds of tripartite entanglement.
This difference is, for example, illustrated by the following interesting property of the W state: if one of the three qubits is lost, the state of the remaining 2-qubit system is still entangled. This robustness of W-type entanglement contrasts strongly with the GHZ state, which is fully separable after loss of one qubit.
The states in the W class can be distinguished from all other 3-qubit states by means of multipartite entanglement measures. In particular, W states have non-zero entanglement across any bipartition,[4] while the 3-tangle vanishes, which is also non-zero for GHZ-type states.[2]
Generalization
The notion of W state has been generalized for qubits[2] and then refers to the quantum superposition with equal expansion coefficients of all possible pure states in which exactly one of the qubits is in an "excited state" , while all other ones are in the "ground state" :
Both the robustness against particle loss and the LOCC-inequivalence with the (generalized) GHZ state also hold for the -qubit W state.
Applications
In systems in which a single qubit is stored in an ensemble of many two-level systems the logical "1" is often represented by the W state, while the logical "0" is represented by the state . Here the W state's robustness against particle loss is a very beneficial property ensuring good storage properties of these ensemble-based quantum memories.[5]
See also
References
- S2CID 55659305.
- ^ S2CID 16636159.
- ^ A pure state of parties is called biseparable, if one can find a partition of the parties in two disjoint subsets and with such that , i.e. is a product statewith respect to the partition .
- ^ A bipartition of the three qubits is any grouping and in which two qubits are considered to belong to the same party. The 3-qubit state can then be considered as a state on and studied with bipartite entanglement measures.
- S2CID 54532771.