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arXiv:1306.5295 · New Journal of Physics

Spatial reference frame agreement in quantum networks

Tanvirul Islam, Loïck Magnin, Brandon Sorg, Stephanie Wehner

Published Jun 17, 2014• 8 citations
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Abstract

In order to communicate information in a quantum network effectively, all network nodes should share a common reference frame. Here, we propose to study how well m nodes in a quantum network can establish a common spatial reference frame from scratch, even though t of them may be arbitrarily faulty. We present a protocol that allows all correctly functioning nodes to agree on a common reference frame as long as they are fully connected and not more than nodes are faulty. Our protocol furthermore has the appealing property that it allows any existing two-node protocol for reference frame agreement to be lifted to a protocol for a quantum network.

DOI
10.1088/1367-2630/16/6/063040

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In order to communicate information in a quantum network effectively, all network nodes should share a common reference frame. Here, we propose to study how well m nodes in a quantum network can establish a common spatial reference frame from scratch, even though t of them may be arbitrarily faulty. We present a protocol that allows all correctly functioning nodes to agree on a common reference frame as long as they are fully connected and not more than nodes are faulty. Our protocol furthermore has the appealing property that it allows any existing two-node protocol for reference frame agreement to be lifted to a protocol for a quantum network.
An efficient implementation of many multiparty protocols for quantum networks requires that all the nodes in the network share a common reference frame. Establishing such a reference frame from scratch is especially challenging in an asynchronous network where network links might have arbitrary delays and the nodes do not share synchronised clocks. In this work, we study the problem of establishing a common reference frame in an asynchronous network of n nodes of which at most t are affected by arbitrary unknown error, and the identities of the faulty nodes are not known. We present a protocol that allows all the correctly functioning nodes to agree on a common reference frame as long as the network graph is complete and not more than nodes are faulty. As the protocol is asynchronous, it can be used with some assumptions to synchronise clocks over a network. Also, the protocol has the appealing property that it allows any existing two-node asynchronous protocol for reference frame agreement to be lifted to a robust protocol for an asynchronous quantum network.
We generalize a quantum communication protocol introduced by Bartlett et al. [New J. Phys. 11, 063013 (2009)], in which two parties communicating do not share a classical reference frame, to the case where changes of their reference frames form a one-dimensional noncompact Lie group. Alice sends to Bob the state ${\ensuremath{\rho}}_{R}\ensuremath{\bigotimes}{\ensuremath{\rho}}_{S}$, where ${\ensuremath{\rho}}_{S}$ is the state of the system Alice wishes to communicate and ${\ensuremath{\rho}}_{R}$ is the state of an ancillary system serving as a token of her reference frame. Because Bob is ignorant of the relationship between his reference frame and Alice's, he will describe the state ${\ensuremath{\rho}}_{R}\ensuremath{\bigotimes}{\ensuremath{\rho}}_{S}$ as an average over all possible reference frames. Bob measures the reference token and applies a correction to the system Alice wished to communicate conditioned on the outcome of the measurement. The recovered state ${\ensuremath{\rho}}_{S}^{\ensuremath{'}}$ is decohered with respect to ${\ensuremath{\rho}}_{S}$, the amount of decoherence depending on the properties of the reference token ${\ensuremath{\rho}}_{R}$. We present an example of this protocol when Alice and Bob do not share a reference frame associated with the one-dimensional translation group and use the fidelity between ${\ensuremath{\rho}}_{S}$ and ${\ensuremath{\rho}}_{S}^{\ensuremath{'}}$ to quantify the success of the recovery operation.
We discuss the aligning of spatial reference frames from a quantum communication complexity perspective. This enables us to analyze multiple rounds of communication and give several simple examples demonstrating tradeoffs between the number of rounds and the type of communication. Using a distributed variant of a quantum computational algorithm, we give an explicit protocol for aligning spatial axes via the exchange of spin-1/2 particles which makes no use of either exchanged entangled states, or of joint measurements. This protocol achieves a worst-case fidelity for the problem of "direction finding" that is asymptotically equivalent to the optimal average case fidelity achievable via a single forward communication of entangled states.
Reference-frame-independent measurement-device-independent quantum key distribution is a promising candidate for building star-type quantum secure networks because it does not require reference alignment and removes all detector-side-channel attacks. However, prior works considered only a symmetric case in which the channels of both users have the same loss. In a realistic quantum secure network, the losses of various channels are likely to be different owing to their geographical locations. In this study, we present an asymmetric protocol for scalable reference-frame-independent measurement-device-independent quantum key distribution networks. By allowing independent adjustments of signal intensities of both users, our protocol provides a higher key rate than previous symmetric protocols in a realistic quantum secure network. The simulation results demonstrate that our protocol works well under realistic experimental conditions and obtains a key rate that is approximately one order of magnitude higher than that of previous methods. Our study paves the way for high-rate quantum secure communication network development.
Quantum networking needs knowledge of the quality of a connection in order for quantum error correction to work. We are designing a classical network protocol to support quantum state analysis procedures such as tomography. This paper sketches the protocol as well as summarizes the fundamental scheme of two-node quantum communication using photons. Our protocol is a master-slave protocol. We show that we need around 2000-3000 (42000-60000) Bell pairs for tomography to achieve F > 0.99 (0.999). These stringent performance requirements result in long bootstrap times for individual network links, and suggest that tomography is inappropriate during the establishment of individual connections across a network.
We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model.