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arXiv:1701.03565

Time Evolution of Quantum Entanglement of an EPR Pair in a Localized Environment

Jia Wang, Xia-Ji Liu, Hui Hu

Published Jan 13, 2017• 0 citations
arXivHTMLPDF

Abstract

The Einstein-Podolsky-Rosen (EPR) pair of qubits plays a critical role in many quantum protocol applications such as quantum communication and quantum teleportation. Due to interactions with the environment, an EPR pair can lose its entanglement and no longer serve as a useful quantum resource. On the other hand, it has been suggested that introducing disorder into environment might help prevent thermalization and improve the preservation of entanglement. Here, we theoretically investigate the time evolution of quantum entanglement of an EPR pair in a random-field XXZ spin chain model in the Anderson localized (AL) and many-body localized (MBL) phase. We find that the entanglement between qubits decreases and approaches a plateau in the AL phase, but shows a power-law decrease after some critical time determined by the interaction strength in the MBL phase. Our findings shed light on applying AL/MBL to improve quantum information storage, and can be used as a practical indicator to distinguish the AL and MBL phase.

DOI
10.25916/sut.26247443.v1

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The Einstein-Podolsky-Rosen (EPR) pair of qubits plays a critical role in many quantum protocol applications such as quantum communication and quantum teleportation. Due to interactions with the environment, an EPR pair can lose its entanglement and no longer serve as a useful quantum resource. On the other hand, it has been suggested that introducing disorder into environment might help prevent thermalization and improve the preservation of entanglement. Here, we theoretically investigate the time evolution of quantum entanglement of an EPR pair in a random-field XXZ spin chain model in the Anderson localized (AL) and many-body localized (MBL) phase. We find that the entanglement between qubits decreases and approaches a plateau in the AL phase, but shows a power-law decrease after some critical time determined by the interaction strength in the MBL phase. Our findings shed light on applying AL/MBL to improve quantum information storage, and can be used as a practical indicator to distinguish the AL and MBL phase.
The Einstein–Podolsky–Rosen (EPR) pair of qubits plays a critical role in many quantum protocol applications such as quantum communication and quantum teleportation. Due to interactions with the environment, an EPR pair can lose its entanglement and no longer serve as a useful quantum resource. On the other hand, it has been suggested that introducing disorder into environment might help prevent thermalization and improve the preservation of entanglement. Here, we theoretically investigate the time evolution of quantum entanglement of an EPR pair in a random-field XXZ spin chain model in the Anderson localized (AL) and many-body localized (MBL) phase. We find that the entanglement between qubits decreases and approaches a plateau in the AL phase, but shows a power-law decrease after some critical time determined by the interaction strength in the MBL phase. Our findings shed light on applying AL/MBL to improve quantum information storage, and can be used as a practical indicator to distinguish the AL and MBL phase.
We investigate the trends of information backflow associated with the dynamics of a sub-part of a disordered spin-1/2 transverse field Heisenberg chain for different regimes of the Hamiltonian. Towards this aim, the decay profile of bipartite entanglement shared between a probe-qubit and a system-qubit (sub-part) of the chain is monitored in time. A clear shift in the trends of the decay profiles of the bipartite entanglement from monotonic in the low-disorder limit to non-monotonic in the moderately large disorder limit occurs due to strong information backflow from the environment (complementary part) to the system-qubit. A connection between environmental interruption caused by the information backflow and the disorder strength is established by examining the entanglement revival frequencies. The growth patterns of the revival frequencies in the localized phase plays an instrumental role to effectively distinguish an interacting system (many-body localized) from its non-interacting (Anderson localized) counterpart.
Quantum networks (QNs) are expected to play a key role in next-generation networks. A QN is comprised of quantum nodes and links (or bonds) representing entangled qubit pairs (EQPs) shared between two nodes. The probability of establishing a pure maximally entangled pair, known as Einstein-Podolsky-Rosen (EPR) pair, between two neighboring nodes represents the linking probability (or bond occupation probability). If such probability exceeds the so-called percolation threshold, the QN exhibits a percolation phenomenon characterized by the emergence of a giant cluster spanning the entire network. In the presence of such a giant cluster, any two arbitrary nodes in the system are connected by a chain of links with a non-zero probability, thus establishing EPR pairs at remote nodes. This work introduces a procedure for obtaining QNs from initially isolated quantum nodes. In the proposed procedure, two copies of EPR pairs are prepared at a source node and two qubits, one from each pair, are sent to a neighboring node through a noisy quantum channel. Then, a pair of mixed quantum states is established between the source node and the neighboring node. By performing local operations and classical communication, an EPR pair can be established between these two nodes with non-zero probability. Repeating this procedure for every pair of source node and neighboring node, a QN exhibiting a percolation phenomenon can be obtained.
In quantum networks, long-distance quantum communication relies on Einstein–Podolsky–Rosen (EPR) pairs. However, EPR pairs undergo decoherence over time, while their on-demand generation incurs latency. Pre-Storing EPR pairs in quantum memories can mitigate this latency, but such memories are costly and scarce resources, making their efficient placement an important design problem. While prior studies have mainly focused on routing or entanglement distribution, the placement of quantum memories under fidelity and purification constraints has received limited attention. In this paper, we propose an optimization framework for quantum memory placement that minimizes the average entanglement generation latency under a limited budget of deployable memories. Simulations across multiple real-world topologies show that our method consistently achieves lower latency than random and centrality-based placements, suggesting its potential to improve the scalability of large-scale quantum communication networks.
Quantum entanglement is the key to quantum communications over considerable distances. The first step for entanglement distribution among quantum communication nodes is to generate link-level Einstein-Podolsky-Rosen (EPR) pairs between adjacent communication nodes. EPR pairs may be continuously generated and stored in a few quantum memories to be ready for utilization by quantum applications. A major challenge is that qubits suffer from unavoidable noise due to their interaction with the environment, which is called decoherence. This decoherence results in the known exponential decay model of the fidelity of the qubits with time, thus, limiting the lifetime of a qubit in a quantum memory and the performance of quantum applications. In this paper, we evaluate the fidelity of the stored EPR pairs under two opposite dynamical and probabilistic phenomena, first, the aforementioned decoherence and second purification, i.e. an operation to improve the fidelity of an EPR pair at the expense of sacrificing another EPR pair. Instead of applying the purification as soon as two EPR pairs are generated, we introduce a Purification scheme Beyond the Generation time (PBG) of two EPR pairs. We analytically show the probability distribution of the fidelity of stored link-level EPR pairs in a system with two quantum memories at each node allowing a maximum of two stored EPR pairs. In addition, we apply a PBG scheme that purifies the two stored EPR pairs upon the generation of an additional one. We finally provide numerical evaluations of the analytical approach and show the fidelity-rate trade-off of the considered purification scheme.
The quantum Internet envisions a network where information is transmitted through entanglement, with Einstein-Podolsky-Rosen (EPR) pairs serving as one of the fundamental carriers. In this work, we propose a framework for dimensioning quantum memories capable of storing distilled EPR pairs useful to transmitting and manage quantum error correcting codes. Using a Markov chain model, we capture the stochastic evolution of stored entangled states in quantum memories, linking memory performance to system parameters such as technology characteristics and initial entanglement fidelity. Building on this framework, we provide analytical tools and design principles for optimizing memory architectures that preserve high-fidelity entanglement over time, ensuring the availability of encoded quantum resources necessary for several operations in future quantum Internet infrastructures transmitting EPR packets.