Quantum Proofs

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in which a quantum state plays the role of a proof (also called a certificate or witness), and is checked by a polynomial-time quantum computation. For some problems, the fact that a quantum proof state could be a superposition over exponentially many classical states appears to offer computational advantages over classical proof strings. In the interactive proof system setting, one may consider a verifier and one or more provers that exchange and process quantum information rather than classical information during an interaction for a given input string, giving rise to quantum complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit some properties from their classical counterparts, they also possess distinct and uniquely quantum features that lead to an interesting landscape of complexity classes based on variants of this model. In this survey we provide an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, we discuss non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class \class{QSZK}, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*.Comment: Survey published by NOW publisher

Distributed Information Bottleneck for a Primitive Gaussian Diamond MIMO Channel

This paper considers the distributed information bottleneck (D-IB) problem for a primitive Gaussian diamond channel with two relays and MIMO Rayleigh fading. The channel state is an independent and identically distributed (i.i.d.) process known at the relays but unknown to the destination. The relays are oblivious, i.e., they are unaware of the codebook and treat the transmitted signal as a random process with known statistics. The bottleneck constraints prevent the relays to communicate the channel state information (CSI) perfectly to the destination. To evaluate the bottleneck rate, we provide an upper bound by assuming that the destination node knows the CSI and the relays can cooperate with each other, and also two achievable schemes with simple symbol-by-symbol relay processing and compression. Numerical results show that the lower bounds obtained by the proposed achievable schemes can come close to the upper bound on a wide range of relevant system parameters

Wireless Network Coding with Local Network Views: Coded Layer Scheduling

One of the fundamental challenges in the design of distributed wireless networks is the large dynamic range of network state. Since continuous tracking of global network state at all nodes is practically impossible, nodes can only acquire limited local views of the whole network to design their transmission strategies. In this paper, we study multi-layer wireless networks and assume that each node has only a limited knowledge, namely 1-local view, where each S-D pair has enough information to perform optimally when other pairs do not interfere, along with connectivity information for rest of the network. We investigate the information-theoretic limits of communication with such limited knowledge at the nodes. We develop a novel transmission strategy, namely Coded Layer Scheduling, that solely relies on 1-local view at the nodes and incorporates three different techniques: (1) per layer interference avoidance, (2) repetition coding to allow overhearing of the interference, and (3) network coding to allow interference neutralization. We show that our proposed scheme can provide a significant throughput gain compared with the conventional interference avoidance strategies. Furthermore, we show that our strategy maximizes the achievable normalized sum-rate for some classes of networks, hence, characterizing the normalized sum-capacity of those networks with 1-local view.Comment: Technical report. A paper based on the results of this report will appea

Achieving Functional Correctness in Large Interconnect Systems.

In today's semi-conductor industry, large chip-multiprocessors and systems-on-chip are being developed, integrating a large number of components on a single chip. The sheer size of these designs and the intricacy of the communication patterns they exhibit have propelled the development of network-on-chip (NoC) interconnects as the basis for the communication infrastructure in these systems. Faced with the interconnect's growing size and complexity, several challenges hinder its effective validation. During the interconnect's development, the functional verification process relies heavily on the use of emulation and post-silicon validation platforms. However, detecting and debugging errors on these platforms is a difficult endeavour due to the limited observability, and in turn the low verification capabilities, they provide. Additionally, with the inherent incompleteness of design-time validation efforts, the potential of design bugs escaping into the interconnect of a released product is also a concern, as these bugs can threaten the viability of the entire system. This dissertation provides solutions to enable the development of functionally correct interconnect designs. We first address the challenges encountered during design-time verification efforts, by providing two complementary mechanisms that allow emulation and post-silicon verification frameworks to capture a detailed overview of the functional behaviour of the interconnect. Our first solution re-purposes the contents of in-flight traffic to log debug data from the interconnect's execution. This approach enables the validation of the interconnect using synthetic traffic workloads, while attaining over 80% observability of the routes followed by packets and capturing valuable debugging information. We also develop an alternative mechanism that boosts observability by taking periodic snapshots of execution, thus extending the verification capabilities to run both synthetic traffic and real-application workloads. The collected snapshots enhance detection and debugging support, and they provide observability of over 50% of packets and reconstructs at least half of each of their routes. Moreover, we also develop error detection and recovery solutions to address the threat of design bugs escaping into the interconnect's runtime operation. Our runtime techniques can overcome communication errors without needing to store replicate copies of all in-flight packets, thereby achieving correctness at minimal area costsPhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/116741/1/rawanak_1.pd

Anonymous transmission in a noisy quantum network using the W state

We consider the task of anonymously transmitting a quantum message in a network. We present a protocol that accomplishes this task using the W state and we analyze its performance in a quantum network where some form of noise is present. We then compare the performance of our protocol with some of the existing protocols developed for the task of anonymous transmission. We show that, in many regimes, our protocol tolerates more noise and achieves higher fidelities of the transmitted quantum message than the other ones. Furthermore, we demonstrate that our protocol tolerates one non-responsive node. We prove the security of our protocol in a semi-active adversary scenario, meaning that we consider an active adversary and a trusted source.Comment: 9 + 12 pages, 9 figure