Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the $W$ state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal $N$-qubit GHZ state to a state arbitrarily close to the ideal $N$-qubit $W$ state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.
Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the W state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal N-qubit GHZ state to a state arbitrarily close to the ideal N-qubit W state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.
We discuss the (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancilla under local operation and classical communication. Whereas any two orthogonal Greenberger-Horne-Zeilinger (GHZ) states taken from the canonical GHZ basis can be cloned with the help of a known GHZ state, surprisingly we find that no two W states can be cloned by using any known three qubit (possibly entangled) state as a blank copy.
We experimentally construct a three-qubit entangled W superposition (WW) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the WW state to the Greenberger-Horne-Zeilinger (GHZ) state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party WW state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the WW state, which is equivalent to the GHZ state under an ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that, although the WW state is interconvertible with the GHZ state, it stores entanglement very differently.
The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. We study this topic in three-qubit systems considering the entanglement classification of stochastic local operations and classical communication (SLOCC). The equivalence under SLOCC divides three-qubit states into separable, biseparable, W, and Greenberger-Horne-Zeilinger (GHZ) classes. The W and GHZ are two subclasses of genuine tripartite entanglement. We adopt the family of GHZ-symmetric states as a research subject, which share the symmetries of the GHZ state and have a complete characterization of SLOCC classes. In the biseparable region (with bipartite entanglement), there exist GHZ-symmetric states that are found to be fully local. In addition, there are bilocal states in both the W and GHZ classes. That is, neither of the subclasses of genuine tripartite entanglement can ensure genuinely tripartite nonlocality.
We introduce a real-valued functional I(n1,n2) of four three-qubit correlations that turns the Greenberger-Horne-Zeilinger (GHZ) algebraic paradox into a quantitative witness of genuine tripartite entanglement. For every three-qubit state ρ and every pair of directions, ∣I(n1,n2;ρ)∣≤2, with equality if and only if n1⊥n2 and ρ is locally unitarily equivalent to the GHZ state. On the five-parameter Acín family, I(x^,y^) depends only on λ0λ4 and is maximised by the GHZ state; for the W state I(x^,y^)=0 and max∣IW∣=35/27. Maximising over independent local orthonormal frames yields a local-unitary invariant measure EGHZ∈[0,1], computable from four three-body Pauli correlators, that equals one exactly on the GHZ orbit and takes the values 35/54 on the W state and 1/2 on product states. We show that EGHZ is not convex: an equal mixture of three biseparable states has EGHZ=14/27, larger than the average 1/2 of its components. We also relate EGHZ to GHZ fidelity witnesses, discuss its behaviour under local operations and classical communication, and outline a generalisation to three qudits via Heisenberg-Weyl operators.
The states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely, the Greenberger-Horne-Zeilinger (GHZ) type and the W type. A state belonging to one of these classes can be stochastically transformed only into a state within the same class by local operations and classical communications. We provide local quantum operations, consisting of the most general two-outcome measurement operators, for the deterministic transformations of three-qubit pure states in which the initial and the target states are in the same class. We explore these transformations, originally having standard GHZ and standard W states, under the local measurement operations carried out by a single party and p (p=2,3) parties (successively). We find a notable result that the standard GHZ state cannot be deterministically transformed to a GHZ-type state in which all its bipartite entanglements are nonzero, i.e., a transformation can be achieved with unit probability when the target state has at least one vanishing bipartite concurrence.