Identifying Pure States

Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert

Stephen Mark Barnett, Anthony Chefles, Igor Jex

Can we establish whether or not two quantum systems have been prepared in the same state? We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to conclusively identify two pure unknown states as being identical, and construct the optimal measurement for conclusively identifying them as being different. We then derive optimal strategies for state comparison when the state of each system is one of two known states.

J. C. A. Barata, Marcos Brum, Victor Chabu +1 more

Subhasish Bag, Sarkar, Ramita, Prasanta Kumar Panigrahi

We propose a straightforward method to determine the maximal entanglement of pure states using the criterion of maximal I-concurrence, a measure of entanglement. The square of concurrence for a bipartition $X|X^\prime$ of a pure state is defined as $E^2_{X| X ^\prime}=2[1-tr({ρ_X}^2)]$. From this, we can infer that the concurrence $E_{X| X ^\prime}$ reaches its maximum when $tr({ρ_X}^2)$ is minimized. Using this approach, we identify numerous Absolutely Maximally Entangled (AME) pure states that exhibit maximal entanglement across all possible bipartitions. Conditions are derived for pure states to achieve maximal mixedness in all bipartitions, revealing that any pure state with an odd number of subsystem coefficients does not meet the AME criterion. Furthermore, we obtain equal maximal multipartite entangled pure states across all bipartitions using our maximal concurrence criterion.

Matthias Englbrecht, Barbara Kraus

Stabilizer states constitute a set of pure states which plays a dominant role in quantum error correction, measurement-based quantum computation, and quantum communication. Central in these applications are the local symmetries of these states. We characterize all local, invertible (unitary and nonunitary) symmetries of arbitrary stabilizer states and provide an algorithm which determines them. We demonstrate the usefulness of these results by showing that the additional local symmetries find applications in entanglement theory and quantum error correction. More precisely, we study a central problem in entanglement theory, which is concerned with the existence of transformations via local operations among pure states. We demonstrate that the identified symmetries enable additional transformations from a stabilizer state to some other multipartite pure state. Furthermore, we demonstrate how the identified symmetries can be used to construct stabilizer codes with diagonal transversal gates.