Dimensionality distinguishers

Christopher King, Daniel Matysiak

We present numerical evidence showing that any three-dimensional subspace of has an orthonormal basis which can be reliably distinguished using one-way LOCC (local operations and classical communication), where a measurement is made first on the three-dimensional part and the result used to select an optimal measurement on the n -dimensional part. We also show that the order of measurement is essential, by providing an example of a three-dimensional subspace of which does not have any basis that can be distinguished by measuring first on the five-dimensional factor.

Stanislav S. Straupe, S. P. Kulik

Zhiwei Song, Lin Chen, Dragomir Ž. Ðoković

We show that every three-dimensional subspace of qutrit-qudit complex or real systems has a distinguishable basis under one-way local projective measurements and classical communication (LPCC). This solves a long-standing open problem proposed in [J. Phys. A, 40, 7937, 2007]. We further construct a three-dimensional space whose locally distinguishable basis is unique and apply the uniqueness property to the task of state transformation. We also construct a three-dimensional locally distinguishable multipartite space assisted with entanglement. On the other hand, we show that four-dimensional indistinguishable bipartite subspace under one-way LPCC exists. Our work offers profound insights and introduces a theoretical tool for understanding the local distinguishability of subspace. As a consequence, every qutrit channel has optimal environment-assisting classical capacity, and the environment-assisted classical capacity of every rank-three channel is at least$\log _{2} 3$. We also show that every two-qutrit state can be converted into a generalized classical state near the quantum-classical boundary by an entanglement-breaking channel.

J. Beugnon

Malte C. Tichy

The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which interpolates between distinguishable particles and identical bosons, and easily extends to mixed initial states. The permanent of the distinguishability matrix, composed of all mutual scalar products of the single-particle mode-functions, emerges as a natural measure for the degree of interference: It yields a bound on the difference between event probabilities for partially distinguishable bosons and the idealized species, and exactly quantifies the degree of bosonic bunching.

Noriaki Horiuchi