Equivalent Representations in Symmetrized Tensors

D. Dubbers, H.‐J. Stöckmann

Lingaraj Sahu, Michael Schürmann, Kalyan B. Sinha

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson–Parthasarathy flow.

Fabian Bohnet-Waldraff, Daniel Braun, O. Giraud

We express the positive-partial-transpose (PPT) separability criterion for symmetric states of multiqubit systems in terms of matrix inequalities based on the recently introduced tensor representation for spin states. We construct a matrix from the tensor representation of the state and show that it is similar to the partial transpose of the density matrix written in the computational basis. Furthermore, the positivity of this matrix is equivalent to the positivity of a correlation matrix constructed from tensor products of Pauli operators. This allows for a more transparent experimental interpretation of the PPT criteria for an arbitrary spin-$j$ state. The unitary matrices connecting our matrix to the partial transpose of the state generalize the so-called magic basis that plays a central role in Wootters' explicit formula for the concurrence of a two-qubit system and the Bell bases used for the teleportation of a one- or two-qubit state.

Ilya G. Kaplan

Edgard Elbaz

Abranches, Juan, Castro, Alicia, Toriumi, Reiko

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that the partition functions of certain self-adjoint models and their complex counterparts are different integral representations of the exact same function. A special case of these equivalences takes a form of newly found dually weighted intermediate field representations, which generalize the standard intermediate field representation. We also find indications of an equivalence between real tensor models and self-transpose tensor models.