Phase boundaries in deterministic dense coding

Abstract

We consider dense coding with partially entangled states on bipartite systems of dimension $d\times d$, studying the conditions under which a given number of messages, $N$, can be deterministically transmitted. It is known that the largest Schmidt coefficient, ${\lambda }_0$, must obey the bound ${\lambda }_0\le d/N$, and considerable empirical evidence points to the conclusion that there exist states satisfying ${\lambda }_0=d/N$ for every $d$ and $N$ except the special cases $N=d+1$ and $N=d^2-1$. We provide additional conditions under which this bound cannot be reached -- that is, when it must be that ${\lambda }_0<d/N$ -- yielding insight into the shapes of boundaries separating entangled states that allow $N$ messages from those that allow only $N-1$. We also show that these conclusions hold no matter what operations are used for the encoding, and in so doing, identify circumstances under which unitary encoding is strictly better than non-unitary.

7 pages, 1 figure

References in corpus (5)

• Not So SuperDense Coding - Deterministic Dense Coding with Partially Entangled States
• Deterministic and Unambiguous Dense Coding
• Deterministic dense coding and entanglement entropy
• Boundary effect of deterministic dense coding
• Non-optimality of unitary operations for dense coding

Cited by in corpus (4)

• Deterministic Quantum Dense Coding Networks
• One-shot conclusive multiport quantum dense coding capacities
• Secure $N$-dimensional Simultaneous Dense Coding and Applications
• The augmented message-matrix approach to deterministic dense coding theory