arXiv subjects

Liangzhong Ruan

Publications and source records attributed to Liangzhong Ruan.

14 recordsLinked to original sources

arXiv2024

Reliable Interval Estimation for the Fidelity of Entangled States in Scenarios with General Noise

Fidelity estimation for entangled states constitutes an essential building block for quality control and error detection in quantum networks. Nonetheless, quantum networks often encounter heterogeneous and correlated noise, leading to excessive uncertainty in the estimated fidelity. In this paper, the uncertainty associated with the estimated fidelity under conditions of general noise is constrained by jointly employing random sampling, a thought experiment, and Bayesian inference, resulting in a credible interval for fidelity that is valid in the presence of general noise. The proposed credible interval incorporates all even moments of the posterior distribution to enhance estimation accuracy. Factors influencing the estimation accuracy are identified and analyzed. Specifically, the issue of excessive measurements is addressed, emphasizing the necessity of properly determining the measurement ratio for fidelity estimation under general noise conditions.

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arXiv2024

Error minimization for fidelity estimation of GHZ states with arbitrary noise

Fidelity estimation is a crucial component for the quality control of entanglement distribution networks. This work studies a scenario in which multiple nodes share noisy Greenberger-Horne-Zeilinger (GHZ) states. Due to the collapsing nature of quantum measurements, the nodes randomly sample a subset of noisy GHZ states for measurement and then estimate the average fidelity of the unsampled states conditioned on the measurement outcome. By developing a fidelity-preserving diagonalization operation, analyzing the Bloch representation of GHZ states, and maximizing the Fisher information, the proposed estimation protocol achieves the minimum mean squared estimation error in a challenging scenario characterized by arbitrary noise and the absence of prior information. Additionally, this protocol is implementation-friendly as it only uses local Pauli operators according to a predefined sequence. Numerical studies demonstrate that, compared to existing fidelity estimation protocols, the proposed protocol reduces estimation errors in both scenarios involving independent and identically distributed (i.i.d.) noise and correlated noise.

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arXiv2022

Minimization of the estimation error for entanglement distribution networks with arbitrary noise

Fidelity estimation is essential for the quality control of entanglement distribution networks. Because measurements collapse quantum states, we consider a setup in which nodes randomly sample a subset of the entangled qubit pairs to measure and then estimate the average fidelity of the unsampled pairs conditioned on the measurement outcome. The proposed estimation protocol achieves the lowest mean squared estimation error in a difficult scenario with arbitrary noise and no prior information. Moreover, this protocol is implementation friendly because it only performs local Pauli operators according to a predefined sequence. Numerical studies show that compared to existing fidelity estimation protocols, the proposed protocol reduces the estimation error in both scenarios with i.i.d. noise and correlated noise.

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arXiv2018

Efficient Entanglement Distillation for Quantum Channels with Polarization Mode Dispersion

Quantum entanglement shared by remote network nodes serves as a valuable resource for promising applications in distributed computing, cryptography, and sensing. However, distributing entanglement with high-quality via fiber optic routes could be challenging due to the various decoherence mechanisms in fibers. In particular, one of the primary polarization decoherence mechanisms in optical fibers is polarization mode dispersion (PMD), which is the distortion of optical pulses by randomly varying birefringences in the system. To mitigate the effect of decoherence in entangled particles, quantum entanglement distillation (QED) algorithms have been proposed. One particular class, the recurrence QED algorithms, stands out because it has relatively relaxed requirements on both the size of the quantum circuits involved and on the initial quality of entanglement in particles. However, because the number of particles required grows exponentially with the number of rounds of distillation, an efficient recurrence algorithm needs to converge quickly. We present a recurrence QED algorithm designed for photonic qubit pairs affected by PMD-degraded channels. Our proposed algorithm achieves the optimal fidelity as well as the optimal success probability (conditional on the optimal fidelity being achieved) in every round of distillation. The attainment of optimal fidelity improves the convergence speed of fidelity with respect to the rounds of distillation from linear to quadratic, and hence significantly reduces the number of distillation rounds. Combined with the fact that the optimal success probability is achieved, the proposed algorithm provides an efficient method to distribute entangled states with high fidelity via optic fibers.

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arXiv2017

Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels

Quantum entanglement serves as a valuable resource for many important quantum operations. A pair of entangled qubits can be shared between two agents by first preparing a maximally entangled qubit pair at one agent, and then sending one of the qubits to the other agent through a quantum channel. In this process, the deterioration of entanglement is inevitable since the noise inherent in the channel contaminates the qubit. To address this challenge, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of implementability and robustness. However, the efficiency of recurrence QED algorithms has not been investigated thoroughly in the literature. This paper put forth two recurrence QED algorithms that adapt to the quantum channel to tackle the efficiency issue. The proposed algorithms have guaranteed convergence for quantum channels with two Kraus operators, which include phase-damping and amplitude-damping channels. Analytical results show that the convergence speed of these algorithms is improved from linear to quadratic and one of the algorithms achieves the optimal speed. Numerical results confirm that the proposed algorithms significantly improve the efficiency of QED.

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arXiv2015

Generalized Interference Alignment --- Part II: Application to Wireless Secrecy

In contrast to its wired counterpart, wireless communication is highly susceptible to eavesdropping due to the broadcast nature of the wireless propagation medium. Recent works have proposed the use of interference to reduce eavesdropping capabilities in wireless wiretap networks. However, the concurrent effect of interference on both eavesdropping receivers (ERs) and legitimate receivers (LRs) has not been thoroughly investigated, and carefully engineering the network interference is required to harness the full potential of interference for wireless secrecy. This two part paper addresses this issue by proposing a generalized interference alignment (GIA) technique, which jointly designs the transceivers at the legitimate partners to impede the ERs without interfering with LRs. In Part I, we have established a theoretical framework for the GIA technique. In Part II, we will first propose an efficient GIA algorithm that is applicable to large-scale networks and then evaluate the performance of this algorithm in stochastic wireless wiretap network via both analysis and simulation. These results reveal insights into when and how GIA contributes to wireless secrecy.

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arXiv2015

Generalized Interference Alignment --- Part I: Theoretical Framework

Interference alignment (IA) has attracted enormous research interest as it achieves optimal capacity scaling with respect to signal to noise ratio on interference networks. IA has also recently emerged as an effective tool in engineering interference for secrecy protection on wireless wiretap networks. However, despite the numerous works dedicated to IA, two of its fundamental issues, i.e., feasibility conditions and transceiver design, are not completely addressed in the literature. In this two part paper, a generalised interference alignment (GIA) technique is proposed to enhance the IA's capability in secrecy protection. A theoretical framework is established to analyze the two fundamental issues of GIA in Part I and then the performance of GIA in large-scale stochastic networks is characterized to illustrate how GIA benefits secrecy protection in Part II. The theoretical framework for GIA adopts methodologies from algebraic geometry, determines the necessary and sufficient feasibility conditions of GIA, and generates a set of algorithms that can solve the GIA problem. This framework sets up a foundation for the development and implementation of GIA.

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arXiv2013

CSI Feedback Reduction for MIMO Interference Alignment

Interference alignment (IA) is a linear precoding strategy that can achieve optimal capacity scaling at high SNR in interference networks. Most of the existing IA designs require full channel state information (CSI) at the transmitters, which induces a huge CSI signaling cost. Hence it is desirable to improve the feedback efficiency for IA and in this paper, we propose a novel IA scheme with a significantly reduced CSI feedback. To quantify the CSI feedback cost, we introduce a novel metric, namely the feedback dimension. This metric serves as a first-order measurement of CSI feedback overhead. Due to the partial CSI feedback constraint, conventional IA schemes can not be applied and hence, we develop a novel IA precoder / decorrelator design and establish new IA feasibility conditions. Via dynamic feedback profile design, the proposed IA scheme can also achieve a flexible tradeoff between the degree of freedom (DoF) requirements for data streams, the antenna resources and the CSI feedback cost. We show by analysis and simulations that the proposed scheme achieves substantial reductions of CSI feedback overhead under the same DoF requirement in MIMO interference networks.

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arXiv2013

Hierarchical Radio Resource Optimization for Heterogeneous Networks with Enhanced Inter-cell Interference Coordination (eICIC)

Interference is a major performance bottleneck in Heterogeneous Network (HetNet) due to its multi-tier topological structure. We propose almost blank resource block (ABRB) for interference control in HetNet. When an ABRB is scheduled in a macro BS, a resource block (RB) with blank payload is transmitted and this eliminates the interference from this macro BS to the pico BSs. We study a two timescale hierarchical radio resource management (RRM) scheme for HetNet with dynamic ABRB control. The long term controls, such as dynamic ABRB, are adaptive to the large scale fading at a RRM server for co-Tier and cross-Tier interference control. The short term control (user scheduling) is adaptive to the local channel state information within each BS to exploit the multi-user diversity. The two timescale optimization problem is challenging due to the exponentially large solution space. We exploit the sparsity in the interference graph of the HetNet topology and derive structural properties for the optimal ABRB control. Based on that, we propose a two timescale alternative optimization solution for the user scheduling and ABRB control. The solution has low complexity and is asymptotically optimal at high SNR. Simulations show that the proposed solution has significant gain over various baselines.

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arXiv2013

Limited Feedback Design for Interference Alignment on MIMO Interference Networks with Heterogeneous Path Loss and Spatial Correlations

Interference alignment is degree of freedom optimal in K -user MIMO interference channels and many previous works have studied the transceiver designs. However, these works predominantly focus on networks with perfect channel state information at the transmitters and symmetrical interference topology. In this paper, we consider a limited feedback system with heterogeneous path loss and spatial correlations, and investigate how the dynamics of the interference topology can be exploited to improve the feedback efficiency. We propose a novel spatial codebook design, and perform dynamic quantization via bit allocations to adapt to the asymmetry of the interference topology. We bound the system throughput under the proposed dynamic scheme in terms of the transmit SNR, feedback bits and the interference topology parameters. It is shown that when the number of feedback bits scales with SNR as C_{s}\cdot\log\textrm{SNR}, the sum degrees of freedom of the network are preserved. Moreover, the value of scaling coefficient C_{s} can be significantly reduced in networks with asymmetric interference topology.

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arXiv2012

The Feasibility Conditions for Interference Alignment in MIMO Networks

Interference alignment (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition matches with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.

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arXiv2012

Interference Alignment for Partially Connected MIMO Cellular Networks

In this paper, we propose an iterative interference alignment (IA) algorithm for MIMO cellular networks with partial connectivity, which is induced by heterogeneous path losses and spatial correlation. Such systems impose several key technical challenges in the IA algorithm design, namely the overlapping between the direct and interfering links due to the MIMO cellular topology as well as how to exploit the partial connectivity. We shall address these challenges and propose a three stage IA algorithm. As illustration, we analyze the achievable degree of freedom (DoF) of the proposed algorithm for a symmetric partially connected MIMO cellular network. We show that there is significant DoF gain compared with conventional IA algorithms due to partial connectivity. The derived DoF bound is also backward compatible with that achieved on fully connected K-pair MIMO interference channels.

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arXiv2011

Dynamic Interference Mitigation for Generalized Partially Connected Quasi-static MIMO Interference Channel

Recent works on MIMO interference channels have shown that interference alignment can significantly increase the achievable degrees of freedom (DoF) of the network. However, most of these works have assumed a fully connected interference graph. In this paper, we investigate how the partial connectivity can be exploited to enhance system performance in MIMO interference networks. We propose a novel interference mitigation scheme which introduces constraints for the signal subspaces of the precoders and decorrelators to mitigate "many" interference nulling constraints at a cost of "little" freedoms in precoder and decorrelator design so as to extend the feasibility region of the interference alignment scheme. Our analysis shows that the proposed algorithm can significantly increase system DoF in symmetric partially connected MIMO interference networks. We also compare the performance of the proposed scheme with various baselines and show via simulations that the proposed algorithms could achieve significant gain in the system performance of randomly connected interference networks.

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arXiv2010

Decentralized Dynamic Hop Selection and Power Control in Cognitive Multi-hop Relay Systems

In this paper, we consider a cognitive multi-hop relay secondary user (SU) system sharing the spectrum with some primary users (PU). The transmit power as well as the hop selection of the cognitive relays can be dynamically adapted according to the local (and causal) knowledge of the instantaneous channel state information (CSI) in the multi-hop SU system. We shall determine a low complexity, decentralized algorithm to maximize the average end-to-end throughput of the SU system with dynamic spatial reuse. The problem is challenging due to the decentralized requirement as well as the causality constraint on the knowledge of CSI. Furthermore, the problem belongs to the class of stochastic Network Utility Maximization (NUM) problems which is quite challenging. We exploit the time-scale difference between the PU activity and the CSI fluctuations and decompose the problem into a master problem and subproblems. We derive an asymptotically optimal low complexity solution using divide-and-conquer and illustrate that significant performance gain can be obtained through dynamic hop selection and power control. The worst case complexity and memory requirement of the proposed algorithm is O(M^2) and O(M^3) respectively, where $M$ is the number of SUs.

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