Deterministic distributed dense coding with stabilizer states

We consider the possibility of using stabilizer states to perform deterministic dense coding among multiple senders and a single receiver. In the model we studied, the utilized stabilizer state is partitioned into several subsystems and then each subsystem is held by a distinct party. We present a sufficient condition for a stabilizer state to be useful for deterministic distributed dense coding with respect to a given partition plan. The corresponding protocol is also constructed. Furthermore, we propose a method to partially solve a more general problem of finding the set of achievable alphabet sizes for an arbitrary stabilizer state with respect to an arbitrary partition plan. Finally, our work provides a new perspective from the stabilizer formalism to view the standard dense coding protocol and also unifies several previous results in a single framework.Comment: 10 pages, no figur

Shared Randomness and Quantum Communication in the Multi-Party Model

We study shared randomness in the context of multi-party number-in-hand communication protocols in the simultaneous message passing model. We show that with three or more players, shared randomness exhibits new interesting properties that have no direct analogues in the two-party case. First, we demonstrate a hierarchy of modes of shared randomness, with the usual shared randomness where all parties access the same random string as the strongest form in the hierarchy. We show exponential separations between its levels, and some of our bounds may be of independent interest. For example, we show that the equality function can be solved by a protocol of constant length using the weakest form of shared randomness, which we call "XOR-shared randomness." Second, we show that quantum communication cannot replace shared randomness in the k-party case, where k >= 3 is any constant. We demonstrate a promise function GP_k that can be computed by a classical protocol of constant length when (the strongest form of) shared randomness is available, but any quantum protocol without shared randomness must send n^Omega(1) qubits to compute it. Moreover, the quantum complexity of GP_k remains n^Omega(1) even if the "second strongest" mode of shared randomness is available. While a somewhat similar separation was already known in the two-party case, in the multi-party case our statement is qualitatively stronger: * In the two-party case, only a relational communication problem with similar properties is known. * In the two-party case, the gap between the two complexities of a problem can be at most exponential, as it is known that 2^(O(c)) log n qubits can always replace shared randomness in any c-bit protocol. Our bounds imply that with quantum communication alone, in general, it is not possible to simulate efficiently even a three-bit three-party classical protocol that uses shared randomness.Comment: 14 pages; v2: improved presentation, corrected statement of Theorem 2.1, corrected typo

The Tuzu Gesar epic : Performance and singers

Different minority groups have different versions of the Gesar epic. Their respective forms differ from the Tibetan version in content, structure, characters, events, and actual performances. This kind of variety is common in Asian oral epic traditions. The Tu people are a unique minority who reside in northwest China with a total population of 200,000. The Gesar epic of this group is found mainly in Tu communities in Gansu and Qinghai provinces. The Tuzu Gesar is performed as a combination of verse and prose. It also shows some differences from the Anduo dialects of Tibetan. As a result of phonetic changes, the Tuzu Gesar has its own structure and follows strict procedures and performance rules. Many native scholars and experts have studied this tradition.Translated by Li Xianting