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Advanced Quantum Technologies

Tradeoff Relations in Quantum Resource Theory

Fei Ming, Dong Wang, Li‐Juan Li, Xiao‐Gang Fan, Xue‐Ke Song, Ye Liu, Jing‐Ling Chen

Published May 13, 2021• 20 citations
Publisher

Abstract

Abstract Entanglement and coherence are deemed as two unreplaceable and important quantum resources in the regime of quantum physics, which are widely applied to quantum information processing and quantum computation. It is therefore natural to ask if there exists any intrinsic relationship between entanglement and coherence. In this work, the authors originally put forward tradeoff relations between intrinsic concurrence and first‐order coherence in the context of an arbitrary three‐qubit state. To do so, an equality relation related to the quantum entanglement and first‐order coherence for arbitrary three‐qubit pure states is derived first, and then extended to present another tradeoff relation regarding arbitrary three‐qubit states. Notably, physical explanation is offered for how coherence migrates in three‐qubit systems from first‐order coherence of a given subsystem to quantum correlations between subsystems. The result shows that the derived tradeoff relations can reveal the complementarity between intrinsic concurrence and first‐order coherence, which provides reliable theoretical basis of transformation and flow for quantum resources.

DOI
10.1002/qute.202100036

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Abstract Entanglement and coherence are deemed as two unreplaceable and important quantum resources in the regime of quantum physics, which are widely applied to quantum information processing and quantum computation. It is therefore natural to ask if there exists any intrinsic relationship between entanglement and coherence. In this work, the authors originally put forward tradeoff relations between intrinsic concurrence and first‐order coherence in the context of an arbitrary three‐qubit state. To do so, an equality relation related to the quantum entanglement and first‐order coherence for arbitrary three‐qubit pure states is derived first, and then extended to present another tradeoff relation regarding arbitrary three‐qubit states. Notably, physical explanation is offered for how coherence migrates in three‐qubit systems from first‐order coherence of a given subsystem to quantum correlations between subsystems. The result shows that the derived tradeoff relations can reveal the complementarity between intrinsic concurrence and first‐order coherence, which provides reliable theoretical basis of transformation and flow for quantum resources.
Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there are direct link between them. And by thinking about this question, we propose a new measure for quantum state that contains concurrence and is called intrinsic concurrence. Interestingly, we discover that the intrinsic concurrence is always complementary to coherence. Note that the intrinsic concurrence is related to the concurrence of a special pure state ensemble. In order to explain the trade-off relation more intuitively, we apply it in some composite systems composed by a single-qubit state coupling four typical noise channels with the aim at illustrating their mutual transformation relationship between their coherence and intrinsic concurrence. This unified trade-off relation will provide more flexibility in exploiting one resource to perform quantum tasks and also provide credible theoretical basis for the interconversion of the two important quantum resources.
Abstract Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there is a direct link between them. In this work, we propose a definition of intrinsic concurrence for two-qubit states. Although the intrinsic concurrence is not a measure of entanglement, it embodies the concurrence of four pure states which are members of a special pure state ensemble for an arbitrary two-qubit state. And we show that intrinsic concurrence is always complementary to first-order coherence. In fact, this relation is an extension of the complementary relation satisfied by two-qubit pure states. Interestingly, we apply the complementary relation in some composite systems composed by a single-qubit state coupling with four typical noise channels respectively, and discover their mutual transformation relation between concurrence and first-order coherence. This universal complementarity provides reliable theoretical basis for the interconversion of the two important quantum resources.
An analytical exploration of the phase decoherence equation of two qubits interacting with a coherent field with dipole–dipole interaction is introduced. The study examines the tradeoff relationships between intrinsic concurrence and first-order coherence in the qubits–cavity system while considering the impacts of decoherence and the interactions among the qubits. We affirm that the relationship between intrinsic concurrence and first-order coherence is valid. Additionally, we demonstrate that the minimum limit of intrinsic concurrence is universally applicable, although the upper limit is typically not. These connections in Heisenberg models can provide a means by which to investigate how quantum resources are allocated in spins, potentially leading to future applications in quantum information processing. It is partially but not completely possible to control the tradeoff relations between intrinsic concurrence and first-order coherence of the two-qubit cavity system; this control might involve actions that influence the system and are reflected in intrinsic concurrence and first-order coherence.
In quantum resource theories (QRTs), evidence of intrinsic connections between coherence and quantum correlations, including Bell nonlocality, entanglement, quantum steering, and so on, exists. However, building these relationships is a vital yet challenging task in multipartite quantum systems. Here, we focus on a unified framework of interpreting the interconversions among coherence and different quantum correlations in tripartite systems. In particular, an exact relation between the generalized geometric measure and the genuinely multipartite concurrence is derived for tripartite entanglement states. Then we obtain the trade-off relation between the first-order coherence and the genuine tripartite entanglement by the genuinely multipartite concurrence and concurrence fill. Furthermore, the trade-off relation between the maximum steering inequality violation and concurrence fill for arbitrary three-qubit states is found. In addition, we investigate the close relation between the maximum steering inequality violation and the first-order coherence. The results show that coherence and quantum correlations are intrinsically related and can be converted to one another in the framework of QRTs.
Entanglement and coherence are two important resources in quantum information theory. A question naturally arises: Is there some connection between them? We prove that the entanglement of formation and the first-order coherence of two-qubit states satisfy an inequality relation. Two-qubit pure state reaches the upper bound of this inequality. A large number of randomly generated states are used to intuitively verify the complementarity between the entanglement of formation and the first-order coherence. We give the maximum accessible coherence of two-qubit states. Our research results will provide a reliable theoretical basis for conversion of the two quantum resources.
Abstract Studying the relations between entanglement and coherence is essential in many quantum information applications. For this, we consider the concurrence, intrinsic concurrence and first-order coherence, and evaluate the proposed trade-off relations between them. In particular, we study the temporal evolution of a general two-qubit XYZ Heisenberg model with asymmetric spin-orbit interaction under decoherence and analyze the trade-off relations of quantum resource theory. For XYZ Heisenberg model, we confirm that the trade-off relation between intrinsic concurrence and first-order coherence holds. Furthermore, we show that the lower bound of intrinsic concurrence is universally valid, but the upper bound is generally not. These relations in Heisenberg models can provide a way to explore how quantum resources are distributed in spins, which may inspire future applications in quantum information processing.