Extendibility limits the performance of quantum processors

Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in other areas of study; e.g., the resource theories of entanglement and coherence have found use and implications in the study of quantum thermodynamics and memory effects in quantum dynamics. In this paper, we introduce the resource theory of unextendibility, which is associated to the inability of extending quantum entanglement in a given quantum state to multiple parties. The free states in this resource theory are the $k$-extendible states, and the free channels are $k$-extendible channels, which preserve the class of $k$-extendible states. We make use of this resource theory to derive non-asymptotic, upper bounds on the rate at which quantum communication or entanglement preservation is possible by utilizing an arbitrary quantum channel a finite number of times, along with the assistance of $k$-extendible channels at no cost. We then show that the bounds we obtain are significantly tighter than previously known bounds for both the depolarizing and erasure channels.Comment: 39 pages, 6 figures, v2 includes pretty strong converse bounds for antidegradable channels, as well as other improvement

Extendibility of Werner States

We investigate the two-sided symmetric extendibility problem of Werner states. The interplay of the unitary symmetry of these states and the inherent bipartite permutation symmetry of the extendibility scenario allows us to map this problem into the ground state problem of a highly symmetric spin-model Hamiltonian. We solve this ground state problem analytically by utilizing the representation theory of SU(d), in particular a result related to the dominance order of Young diagrams in Littlewood-Richarson decompositions. As a result, we obtain necessary and sufficient conditions for the extendibility of Werner states for arbitrary extension size and local dimension. Interestingly, the range of extendible states has a non-trivial trade-off between the extension sizes on the two sides. We compare our result with the two-sided extendibility problem of isotropic states, where there is no such trade-off.Comment: 5+5 pages, 4 fig

ToPoliNano: Nanoarchitectures Design Made Real

Many facts about emerging nanotechnologies are yet to be assessed. There are still major concerns, for instance, about maximum achievable device density, or about which architecture is best fit for a specific application. Growing complexity requires taking into account many aspects of technology, application and architecture at the same time. Researchers face problems that are not new per se, but are now subject to very different constraints, that need to be captured by design tools. Among the emerging nanotechnologies, two-dimensional nanowire based arrays represent promising nanostructures, especially for massively parallel computing architectures. Few attempts have been done, aimed at giving the possibility to explore architectural solutions, deriving information from extensive and reliable nanoarray characterization. Moreover, in the nanotechnology arena there is still not a clear winner, so it is important to be able to target different technologies, not to miss the next big thing. We present a tool, ToPoliNano, that enables such a multi-technological characterization in terms of logic behavior, power and timing performance, area and layout constraints, on the basis of specific technological and topological descriptions. This tool can aid the design process, beside providing a comprehensive simulation framework for DC and timing simulations, and detailed power analysis. Design and simulation results will be shown for nanoarray-based circuits. ToPoliNano is the first real design tool that tackles the top down design of a circuit based on emerging technologie

Testing symmetry on quantum computers

Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian realizing a time evolution are not useful for timekeeping during that evolution, and bipartite states that are highly extendible are not strongly entangled and thus not useful for basic tasks like teleportation. Motivated by this perspective, this paper details several quantum algorithms that test the symmetry of quantum states and channels. For the case of testing Bose symmetry of a state, we show that there is a simple and efficient quantum algorithm, while the tests for other kinds of symmetry rely on the aid of a quantum prover. We prove that the acceptance probability of each algorithm is equal to the maximum symmetric fidelity of the state being tested, thus giving a firm operational meaning to these latter resource quantifiers. Special cases of the algorithms test for incoherence or separability of quantum states. We evaluate the performance of these algorithms on choice examples by using the variational approach to quantum algorithms, replacing the quantum prover with a parameterized circuit. We demonstrate this approach for numerous examples using the IBM quantum noiseless and noisy simulators, and we observe that the algorithms perform well in the noiseless case and exhibit noise resilience in the noisy case. We also show that the maximum symmetric fidelities can be calculated by semi-definite programs, which is useful for benchmarking the performance of these algorithms for sufficiently small examples. Finally, we establish various generalizations of the resource theory of asymmetry, with the upshot being that the acceptance probabilities of the algorithms are resource monotones and thus well motivated from the resource-theoretic perspective.Comment: v3: 51 pages, 41 figures, 31 tables, final version accepted for publication in Quantum Journa

Extendibility of bosonic Gaussian states

Extendibility of bosonic Gaussian states is a key issue in continuous-variable quantum information. We show that a bosonic Gaussian state is k-extendible if and only if it has a Gaussian k-extension, and we derive a simple semidefinite program, whose size scales linearly with the number of local modes, to efficiently decide k-extendibility of any given bosonic Gaussian state. When the system to be extended comprises one mode only, we provide a closed-form solution. Implications of these results for the steerability of quantum states and for the extendibility of bosonic Gaussian channels are discussed. We then derive upper bounds on the distance of a k-extendible bosonic Gaussian state to the set of all separable states, in terms of trace norm and R'enyi relative entropies. These bounds, which can be seen as "Gaussian de Finetti theorems," exhibit a universal scaling in the total number of modes, independently of the mean energy of the state. Finally, we establish an upper bound on the entanglement of formation of Gaussian k-extendible states, which has no analogue in the finite-dimensional setting

LBSim: A simulation system for dynamic load-balancing algorithms for distributed systems.

In a distributed system consisting of autonomous computational units, the total computational power of all the units needs to be utilized efficiently by applying suitable load-balancing policies. For accomplishing the task, a large number of load balancing algorithms have been proposed in the literature. To facilitate the performance study of each of these load-balancing strategies, simulation has been widely used. However comparison of the load balancing algorithms becomes difficult if a different simulator is used for each case. There have been few studies on generalized simulation of load-balancing algorithms in distributed systems. Most of the simulation systems address the experiments for some particular load-balancing algorithms, whereas this thesis aims to study the simulation for a broad range of algorithms. After the characterization of the distributed systems and the extraction of the common components of load-balancing algorithms, a simulation system, called LBSim, has been built. LBSim is a generalized event-driven simulator for studying load-balancing algorithms with coarse-grained applications running on distributed networks of autonomous processing nodes. In order to verify that the simulation model can represent actual systems reasonably well, we have validated LBSim both qualitatively and quantitatively. As a toolkit of simulation, LBSim programming libraries can be reused to implement load-balancing algorithms for the purpose of performance measurement and analysis from different perspectives. As a framework of algorithm simulation can be extended with a moderate effort by following object-oriented methodology, to meet any new requirements that may arise in the future.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .D8. Source: Masters Abstracts International, Volume: 43-05, page: 1747. Adviser: A. K. Aggarwal. Thesis (M.Sc.)--University of Windsor (Canada), 2004

Asymptotic performance of port-based teleportation

Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number $N$ of ports, the error of the optimal protocol is proportional to the inverse square of $N$. We prove this by deriving an achievability bound, obtained by relating the corresponding optimization problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered simplex. We also give an improved converse bound of matching order in the number of ports. In addition, we determine the leading-order asymptotics of PBT variants defined in terms of maximally entangled resource states. The proofs of these results rely on connecting recently-derived representation-theoretic formulas to random matrix theory. Along the way, we refine a convergence result for the fluctuations of the Schur-Weyl distribution by Johansson, which might be of independent interest.Comment: 68 pages, 4 figures; comments welcome! v2: minor fixes, added plots comparing asymptotic expansions to exact formulas, code available at https://github.com/amsqi/port-base

Practical limitations on robustness and scalability of quantum Internet

As quantum theory allows for information processing and computing tasks that otherwise are not possible with classical systems, there is a need and use of quantum Internet beyond existing network systems. At the same time, the realization of a desirably functional quantum Internet is hindered by fundamental and practical challenges such as high loss during transmission of quantum systems, decoherence due to interaction with the environment, fragility of quantum states, etc. We study the implications of these constraints by analyzing the limitations on the scaling and robustness of quantum Internet. Considering quantum networks, we present practical bottlenecks for secure communication, delegated computing, and resource distribution among end nodes. Motivated by the power of abstraction in graph theory (in association with quantum information theory), we consider graph-theoretic quantifiers to assess network robustness and provide critical values of communication lines for viable communication over quantum Internet. In particular, we begin by discussing limitations on usefulness of isotropic states as device-independent quantum key repeaters which otherwise could be useful for device-independent quantum key distribution. We consider some quantum networks of practical interest, ranging from satellite-based networks connecting far-off spatial locations to currently available quantum processor architectures within computers, and analyze their robustness to perform quantum information processing tasks. Some of these tasks form primitives for delegated quantum computing, e.g., entanglement distribution and quantum teleportation. For some examples of quantum networks, we present algorithms to perform different quantum network tasks of interest such as constructing the network structure, finding the shortest path between a pair of end nodes, and optimizing the flow of resources at a node.Comment: Happy about the successful soft landing of Chandrayaan-3 on the moon by ISRO. 35 pages, 32 figures. Preliminary versio

User evaluation of the performance of information systems

Information technologies (IT) are considered the primary survival factor for many organizations and the most critical success factor in businesses today. To justify the necessary investment in IT, user evaluation of information systems\u27 performance in organizations is a key consideration. This research investigated a comprehensive and convenient means for end users to assess this performance. Among the existing theories and models on the evaluation of information system performance based on intrinsic technological properties, the Web of System Performance (WOSP) model provides the most comprehensive basis for information system evaluation, and therefore merited further investigation. The research question was how well the eight WOSP performance criteria, namely functionality, usability, flexibility, reliability, security, extendibility, connectivity, and privacy, applied in the context of an individual evaluating one or more information systems for use by an organization. For this, it was important to show that, while these performance criteria were abstract concepts, they can be established and identified clearly, in a manner that is valid in the sense of the meaning and that users would consider important. Illustrative statements for each of the eight criteria were therefore obtained, which users were asked to evaluate. Next, it was necessary to show that users prefer the choice of the eight WOSP criteria to the current dominant instrument for evaluation when evaluating software. This was done using a preference questionnaire where subjects rated both the WOSP model and an alternative means of evaluation along various dimensions, the results being compared by statistical analysis. Finally, it was necessary to show that users rate at least three of the WOSP criteria as being important for evaluating information systems. For this, conjoint analysis was used. A browser was selected as the experimental software for this research. The results showed that users found illustrative statements clear, valid and important for the evaluation of browsers. They also preferred using the WOSP model for the evaluation of browsers over TAM, the current dominant model. Finally, while users attached different levels of importance to the various performance criteria for the selection of browsers, five of the criteria were important to a significant degree