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It is well known that quantum states that can be transformed into each other by local unitary transformations are equal from the information theoretic point of view. This defines equivalence classes of states and allows one to write any state with the minimal number of parameters called the canonical form of the state. We define the equivalence classes of local measurements such that local operations which transform states from one equivalence class into another with the same probability are equivalent. This equivalence relation allows one to write the operators with the minimal number of parameters, which we call canonical operators, and hence the use of the canonical operators simplifies the optimal manipulation of quantum states. We use the canonical local operators for the concentration of three-qubit Greenberger-Horne-Zeilinger states and obtain the optimal concentration protocols in terms of the unitary invariants of quantum states, namely, the bipartite concurrences and the three-tangle.
The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. Existing studies on this topic to date were limited to the entanglement classification according to the numbers of particles
In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is suf
We propose a probabilistic quantum cloning scheme using Greenberger-Horne-Zeilinger states, Bell basis measurements, single-qubit unitary operations and generalized measurements, all of which are within the reach of current technology. Compared to an
The $N$-qubit Greenberger-Horne-Zeilinger (GHZ) states are the maximally entangled states of $N$ qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus h
Bells theorem shows a profound contradiction between local realism and quantum mechanics on the level of statistical predictions. It does not involve directly Einstein-Podolsky-Rosen (EPR) correlations. The paradox of Greenberger-Horne-Zeilinger (GHZ