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arXiv:2211.14898 · Physical Review A

Entanglement-assisted quantum speedup: Beating local quantum speed limits

Farha Yasmin, Jan Sperling

Published Jul 8, 2024• 6 citations
arXivHTMLPDF

Abstract

Research in quantum information science aims to surpass the scaling limitations of classical information processing. From a physicist's perspective, performance improvement involves a physical speedup in the quantum domain, achieved by dynamically exploiting quantum correlations. In this study, speed limits in interacting quantum systems are derived by comparing the rates of change in actual quantum dynamics with the quasiclassical evolution confined to the manifold of nonentangled separable states. The utility of the resulting bounds on entanglement-assisted speedup is demonstrated on bipartite qubit systems, bipartite qudit systems, as well as a complex multimode systems. Specifically, the proposed speed limits provide a tight bound on quantum speed advantage, including a quantum gain that can scale exponentially with the system's size. Extensions of the results to open systems and measurable witnesses are discussed.

DOI
10.1103/physreva.110.012424

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Research in quantum information science aims to surpass the scaling limitations of classical information processing. From a physicist's perspective, performance improvement involves a physical speedup in the quantum domain, achieved by dynamically exploiting quantum correlations. In this study, speed limits in interacting quantum systems are derived by comparing the rates of change in actual quantum dynamics with the quasiclassical evolution confined to the manifold of nonentangled separable states. The utility of the resulting bounds on entanglement-assisted speedup is demonstrated on bipartite qubit systems, bipartite qudit systems, as well as a complex multimode systems. Specifically, the proposed speed limits provide a tight bound on quantum speed advantage, including a quantum gain that can scale exponentially with the system's size. Extensions of the results to open systems and measurable witnesses are discussed.
The speed limit on entanglement is defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and trace-distance entanglement, for unitary and arbitrary quantum dynamics, where we assume that the dynamics of the closest separable state can be approximately described by the closest separable dynamics of the actual dynamics of the system. For the unitary dynamics of isolated bipartite systems which are described by pure states, the rate of entanglement production is bounded by the product of fluctuations of the system's driving Hamiltonian and the surprisal operator, with an additional term reflecting the time-dependent nature of the closest separable state. Removing restrictions on the purity of the input and on the unitarity of the evolution, the two terms in the bound get suitably altered. Furthermore, we find a lower bound on the time required to generate or degrade a certain amount of entanglement by arbitrary quantum dynamics. We demonstrate the tightness of our speed limits on entanglement by considering quantum processes of practical interest.
Quantum speed limits, establishing fundamental thresholds for the speed of quantum processes, are central to a wide spectrum of applications of quantum science, ranging from speeding up gate operations in quantum computations and optimizing communication channels to unraveling the rate at which correlations can propagate within many-body systems. In the quest to tailor optimal quantum dynamical speeds, the role of quantum entanglement has been showcased in specific instances. However, a robust universal link between system entanglement and its dynamical speed remains elusive. Here, we formulate the genuine contribution of quantum entanglement by developing universal criteria determining this speed enhancement within a quantum system. Specifically, we establish an upper limit that rigorously bounds the speed of the dynamical evolution of separable states, providing an unattainable speed threshold for these states. Our findings underscore the capacity of quantum entanglement to surpass this limit, demonstrating its capability as a resource for enhancing dynamical speed of the system.
Quantum speed limit is bound on the minimum time a quantum system requires to evolve from an initial state to final state under a given dynamical process. It sheds light on how fast a desired state transformation can take place, which is pertinent for design and control of quantum technologies. In this paper, we derive speed limits on correlations such as entanglement, Bell-CHSH correlation, and quantum mutual information of quantum systems evolving under dynamical processes. Our main result is a speed limit on an entanglement monotone called negativity, which holds for arbitrary-dimensional bipartite quantum systems and processes. Another entanglement monotone which we consider is the concurrence. To illustrate the efficacy of our speed limits, we analytically and numerically compute the speed limits on the negativity, concurrence, and Bell-CHSH correlation for various quantum processes of practical interest. We are able to show that, for practical examples we have considered, some of the speed limits we derived are actually attainable and hence these bounds can be considered to be tight.
We construct a general measure for detecting the quantum speedup in both closed and open systems. The speed measure is based on the changing rate of the position of quantum states on a manifold with appropriate monotone Riemannian metrics. Any increase in speed is a clear signature of dynamical speedup. To clarify the mechanisms for quantum speedup, we first introduce the concept of longitudinal and transverse types of speedup: the former stems from the time evolution process itself with fixed initial conditions, while the latter is a result of adjusting initial conditions. We then apply the proposed measure to several typical closed and open quantum systems, illustrating that quantum coherence (or entanglement) and the memory effect of the environment together can become resources for longitudinally or transversely accelerating dynamical evolution under specific conditions and assumptions.
We show how quantum correlations allow us to break the local speed limits of physical processes using only local measurements and classical communication between two parties that share an entangled state. Inequalities that bound the minimal time of evolution of a quantum state by energy fluctuations can be violated in the presence of steering by conditioning on the measurement outcomes of a remote system. Our results open up pathways for studying how quantum correlations influence the dynamical properties of states and observables. Published by the American Physical Society 2024
This paper explores the potential of quantum entanglement for radically transforming memory access paradigms. The core premise is that leveraging the non-local correlations inherent in entangled quantum states can surpass the limitations imposed by classical physics on data retrieval and modification speeds. We propose a novel architecture where data is encoded across multiple quantum bits, utilizing entanglement to facilitate instantaneous data access from disparate physical locations. This approach aims to circumvent the inherent latency associated with conventional memory systems, offering the theoretical possibility of achieving speeds exceeding those attainable with classical methods. The paper details the conceptual framework, outlining the key mathematical relationships and considerations necessary for implementing such a system. We present a foundational model for quantifying the potential speedup, incorporating factors such as entanglement fidelity and the number of entangled qubits involved. Finally, we discuss the challenges and future research directions associated with realizing entanglement-based memory.