Interaction in Quantum Communication

In some scenarios there are ways of conveying information with many fewer, even exponentially fewer, qubits than possible classically. Moreover, some of these methods have a very simple structure--they involve only few message exchanges between the communicating parties. It is therefore natural to ask whether every classical protocol may be transformed to a ``simpler'' quantum protocol--one that has similar efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity. This, in particular, proves a round hierarchy theorem for quantum communication complexity, and implies, via a simple reduction, an Omega(N^{1/k}) lower bound for k message quantum protocols for Set Disjointness for constant k. Enroute, we prove information-theoretic lemmas, and define a related measure of correlation, the informational distance, that we believe may be of significance in other contexts as well.Comment: 35 pages. Uses IEEEtran.cls, IEEEbib.bst. Submitted to IEEE Transactions on Information Theory. Strengthens results in quant-ph/0005106, quant-ph/0004100 and an earlier version presented in STOC 200

Spin State Transfer in Laterally Coupled Quantum Dot Chains with Disorders

Quantum dot arrays are a promising media for transferring quantum information between two distant points without resorting to mobile qubits. Here we study two most common disorders namely, hyperfine interaction and exchange coupling fluctuations, in quantum dot arrays and their effects on quantum communication through these chains. Our results show that the hyperfine interaction is more destructive than the exchange coupling fluctuations. The average optimal time for communication is not affected by any disorder in the system and our simulations show that anti-ferromagnetic chains are much more resistive than the ferromagnetic ones against both kind of disorders. Even when time modulation of a coupling and optimal control is employed to improve the transmission, the anti-ferromagnetic chain performs much better. We have assumed the quasi-static approximation for hyperfine interaction and time dependent fluctuations in the exchange couplings. Particularly, for studying exchange coupling fluctuations we have considered the static disorder, white noise and $1/f$ noise.Comment: 10 pages, 12 figures. Comments are welcome

Bidirectional coherent classical communication

A unitary interaction coupling two parties enables quantum communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and backward communication. Our first result shows that for any bipartite unitary gate, coherent classical communication is no more difficult than classical communication -- they have the same achievable rate regions. Previously this result was known only for the unidirectional capacities (i.e., the boundaries of the tradeoff). We then relate the tradeoff curve for two-way coherent communication to the tradeoff for two-way quantum communication and the tradeoff for coherent communiation in one direction and quantum communication in the other.Comment: 11 pages, v2 extensive modification and rewriting of the main proof, v3 published version with only a few more change

Continuous-variable quantum non-demolishing interaction at a distance

A feasible setup of continuous-variable (CV) quantum non-demolishing (QND) interaction at a distance is proposed. If two distant experimentalists are able to locally perform identical QND interactions then the proposed realization requires only a single quantum channel and classical communication between them. A possible implementation of the proposed setup in recent quantum optical laboratories is discussed and an influence of Gaussian noise in the quantum channel on a quality of the implementation is analyzed. An efficient realization of the QND interaction at a distance can be a basic step to possible distributed quantum CV experiments between the distant laboratories.Comment: 5 pages, 2 figure

Quantum Computation by Communication

We present a new approach to scalable quantum computing--a ``qubus computer''--which realises qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode. The qubits could be ``static'' matter qubits or ``flying'' optical qubits, but the scheme we focus on here is particularly suited to matter qubits. There is no requirement for direct interaction between the qubits. Universal two-qubit quantum gates may be effected by schemes which involve measurement of the bus mode, or by schemes where the bus disentangles automatically and no measurement is needed. In effect, the approach integrates together qubit degrees of freedom for computation with quantum continuous variables for communication and interaction.Comment: final published versio