Together with Jonathan Oppenheim and Andreas Winter, he discovered quantum state-merging and used this primitive to show that quantum information could be negative. He also co-discovered the Peres-Horodecki criterion for testing whether a state is entangled, and used it to find bound entanglement together with his brother Paweł Horodecki and father Ryszard Horodecki. He co-discovered with Jonathan Oppenheim, Paweł Horodecki and Karol Horodecki that secret key can be drawn from some bound entangled states. Together with Fernando Brandao he proved that every one-dimensional quantum state with a finite correlation length obeys an area law for entanglement entropy.
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