W state
Encyclopedia
The W state is an entangled
quantum state of three qubits which has the following shape
and which is remarkable for representing a specific type of multipartite entanglement and for occurring in several applications in quantum information theory.
) which cannot be transformed (not even probabilistically) into each other by local quantum operations
. 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 Greenberger-Horne-Zeilinger state
which is fully separable after loss of one qubit.
The states in the W class can be distinguished from all other three-qubit states by means of multipartite entanglement measures. In particular, W states have non-zero entanglement across any bipartition while the 3-tangle vanishes, which is also non-zero for GHZ-type states.
qubits and then refers to the quantum superpostion with equal expansion coefficients of all possible pure states in which exactly one of the qubits 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.
. Here the W state's robustness against particle loss is a very beneficial property ensuring good storage properties of these ensemble based quantum memories.
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
quantum state of three qubits which has the following shape
and which is remarkable for representing a specific type of multipartite entanglement and for occurring in several applications in quantum information theory.
Properties
The W state is the representative of one of the two non-biseparable classes of three-qubit states (the other being the GHZ stateGreenberger-Horne-Zeilinger state
In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger state is a certain type of entangled quantum state which involves at least three subsystems . It was first studied by D. Greenberger, M.A. Horne and Anton Zeilinger in 1989...
) which cannot be transformed (not even probabilistically) into each other by local quantum operations
LOCC
LOCC, or Local Operations and Classical Communication, is a method in quantum information theory where a local operation is performed on part of the system, and where the result of that operation is "communicated" classically to another part where usually another local operation is performed...
. 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 Greenberger-Horne-Zeilinger state
Greenberger-Horne-Zeilinger state
In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger state is a certain type of entangled quantum state which involves at least three subsystems . It was first studied by D. Greenberger, M.A. Horne and Anton Zeilinger in 1989...
which is fully separable after loss of one qubit.
The states in the W class can be distinguished from all other three-qubit states by means of multipartite entanglement measures. In particular, W states have non-zero entanglement across any bipartition while the 3-tangle vanishes, which is also non-zero for GHZ-type states.
Generalization
The notion of W state has been generalized for qubits and then refers to the quantum superpostion with equal expansion coefficients of all possible pure states in which exactly one of the qubits 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.