Remote preparation of quantum states

Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a trade-off between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this "universal" formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact trade-off curve for arbitrary ensembles of pure states and pure entangled states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical trade-off for quantum data compression. The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.Comment: 21 pages plus 2 figures (eps), revtex4. v2 corrects some errors and adds obliviousness discussion. v3 has section VI C deleted and various minor oversights correcte

Generalized Remote Preparation of Arbitrary mm-qubit Entangled States via Genuine Entanglements

Herein, we present a feasible, general protocol for quantum communication within a network via generalized remote preparation of an arbitrary $m$-qubit entangled state designed with genuine tripartite Greenberger--Horne--Zeilinger-type entangled resources. During the implementations, we construct novel collective unitary operations; these operations are tasked with performing the necessary phase transfers during remote state preparations. We have distilled our implementation methods into a five-step procedure, which can be used to faithfully recover the desired state during transfer. Compared to previous existing schemes, our methodology features a greatly increased success probability. After the consumption of auxiliary qubits and the performance of collective unitary operations, the probability of successful state transfer is increased four-fold and eight-fold for arbitrary two- and three-qubit entanglements when compared to other methods within the literature, respectively. We conclude this paper with a discussion of the presented scheme for state preparation, including: success probabilities, reducibility and generalizability.Comment: 16 pages, 3 figures, 3 tables, Accepted to Entrop

Conference Key Agreement and Quantum Sharing of Classical Secrets with Noisy GHZ States

We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then consider the applications of our distillation schemes for two cryptographic tasks--namely, (a) conference key agreement and (b) quantum sharing of classical secrets. In particular, we construct ``prepare-and-measure'' protocols. Also we study the yield of those protocols and the threshold value of the fidelity above which the protocols can function securely. Surprisingly, our protocols will function securely even when the initial state does not violate the standard Bell-inequalities for GHZ states. Experimental realization involving only bi-partite entanglement is also suggested.Comment: 5 pages, to appear in Proc. 2005 IEEE International Symposium on Information Theory (ISIT 2005, Adelaide, Australia

The role of environmental correlations in the non-Markovian dynamics of a spin system

We put forward a framework to study the dynamics of a chain of interacting quantum particles affected by individual or collective multi-mode environment, focussing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environmental system magnifies the non-Markovian nature of the chain's dynamics, giving rise to structures in figures of merit such as entanglement and purity that are not observed under a separable multi-mode environment. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest.Comment: 9 pages, 12 figure

The impossibility of non-signaling privacy amplification

Barrett, Hardy, and Kent have shown in 2005 that protocols for quantum key agreement exist the security of which can be proven under the assumption that quantum or relativity theory is correct. More precisely, this is based on the non-local behavior of certain quantum systems, combined with the non-signaling postulate from relativity. An advantage is that the resulting security is independent of what (quantum) systems the legitimate parties' devices operate on: they do not have to be trusted. Unfortunately, the protocol proposed by Barrett et al. cannot tolerate any errors caused by noise in the quantum channel. Furthermore, even in the error-free case it is inefficient: its communication complexity is Theta(1/epsilon) when forcing the attacker's information below epsilon, even if only a single key bit is generated. Potentially, the problem can be solved by privacy amplification of relativistic - or non-signaling - secrecy. We show, however, that such privacy amplification is impossible with respect to the most important form of non-local behavior, and application of arbitrary hash functions.Comment: 24 pages, 2 figure