Research on the Collaboration between Quantum Mechanics and Information Processing

我们推导出了一个公式，该公式确定了每条消息的最佳量子比特数，从而允许对混合态集合携带的量子信息进行渐近忠实的压缩。混合状态集确定了将希尔伯特空间分解为冗余部分和不可约部分。去掉冗余后，最优压缩比由约化系综的von Neumann熵给出，我们还研究了多量子比特系统之间的纠缠共享，特别是在大量子比特限制下的行为。量子纠缠不可能在任意数量的量子比特之间无限共享。随着N量子比特系统中纠缠对数目的增加，二体纠缠度减小。我们分析了一个由N个量子比特组成的系统，其中任意一对粒子是纠缠的。我们证明了任意一对量子比特之间的最大纠缠度(用并发度测量)为2/N。当量子比特处于纯对称(相对于排列)态时，只有一个量子比特处于基态|0&gt；，其他量子比特处于基态|1&gt；，就可以实现这个紧束缚。

We derived a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a decomposition of the Hilbert space into the redundant part and the irreducible part. After removing the redundancy, the optimal compression rate is shown to be given by the von Neumann entropy of the reduced ensemble.We also investigated entanglement sharing among multi-qubit systems, especially its behavior in the limit of large number qubits. Quantum entanglement cannot be unlimitedly shared among an arbitrary number of qubits. The degree of bipartite entanglement decreases as the number of entangled pairs in an N-qubit system increases. We analyze a system of N qubits in which an arbitrary pair of particles is entangled. We show that the maximum degree of entanglement (measured in the concurrence) between any pair of qubits is 2/N. This tight bound can be achieved when the qubits are prepared in a pure symmetric (with respect to permutations) state with just one qubit in the basis state |0> and the others in the basis state |1> .