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Journal of Physics B Atomic Molecular and Optical Physics

Entanglement distribution via noisy quantum channels

Wang Qiong, Mei-Yuan Tan, Yun Liu, Hao‐Sheng Zeng

Published Jun 1, 2009• 18 citations
Publisher

Abstract

We investigate the change of entanglement for distributing an arbitrarily entangled two-qubit pure state via three typical kinds of noisy quantum channels—amplitude damping, phase damping and depolarizing quantum channels. We find that for one-qubit transmission, the output distant entanglement (measured by concurrence) reduces proportionately with respect to its initial amount, and the entanglement-decay ratio is determined only by the noisy characteristics of quantum channels. For two-qubit transmission, the rule of the entanglement change is complex. For phase damping quantum channels, the four Bell states and are all the optimal entanglement-distribution (OED) input states. But for amplitude damping quantum channels, only |ψ ± ⟩ are the OED input. For depolarizing quantum channels, and in the case of symmetrical quantum channels, the four Bell states are still the OED input. We also discuss the problem of entanglement sudden death (ESD) and find that for all the three types of quantum channels, ESD can be found.

DOI
10.1088/0953-4075/42/12/125503

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We investigate the change of entanglement for distributing an arbitrarily entangled two-qubit pure state via three typical kinds of noisy quantum channels—amplitude damping, phase damping and depolarizing quantum channels. We find that for one-qubit transmission, the output distant entanglement (measured by concurrence) reduces proportionately with respect to its initial amount, and the entanglement-decay ratio is determined only by the noisy characteristics of quantum channels. For two-qubit transmission, the rule of the entanglement change is complex. For phase damping quantum channels, the four Bell states and are all the optimal entanglement-distribution (OED) input states. But for amplitude damping quantum channels, only |ψ ± ⟩ are the OED input. For depolarizing quantum channels, and in the case of symmetrical quantum channels, the four Bell states are still the OED input. We also discuss the problem of entanglement sudden death (ESD) and find that for all the three types of quantum channels, ESD can be found.
This paper investigates the change of entanglement for transmitting an arbitrarily entangled two-qubit pure state via one of three typical kinds of noisy quantum channels: amplitude damping quantum channel, phase damping quantum channel and depolarizing quantum channel. It finds, in all these three cases, that the output distant entanglement (measured by concurrence) reduces proportionately with respect to its initial amount, and the decaying ratio is determined only by the noisy characteristics of quantum channels and independent of the form of initial input state.
Abstract Based on the quantum technique of environment-assisted measurement and quantum measurement reversal, we systematically investigate the restoration of quantum entanglement for distributing a two-qubit pure state via three typical kinds of noisy quantum channels-amplitude damping, phase damping and depolarizing quantum channels. Special attention is paid to the unsymmetrical two-qubit arbitrarily entangled states transmission. The analytical or numerical simulations results show that for arbitrarily one-qubit entangled state or two-qubit states transmission, the output distant entanglement could be drastically restored to the initial value in all these three cases.
In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.
We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.
Entanglement distribution is a crucial problem in quantum information science, owing to the essential role that entanglement plays in enabling advanced quantum protocols, including quantum teleportation and quantum cryptography. We investigate strategies for distributing quantum entanglement between two distant parties through noisy quantum channels. Specifically, we compare two configurations: one where the entanglement source is placed at the midpoint of the communication line, and another where it is located at one end. For certain families of qubit channels we show analytically that the midpoint strategy is optimal. Based on extensive numerical analysis, we conjecture that this strategy is generally optimal for all qubit channels. Focusing on the midpoint configuration, we develop semidefinite programming (SDP) techniques to assess whether entanglement can be successfully distributed through the network, and to quantify the amount of entanglement that can be distributed in the process. In many relevant cases the SDP formulation reliably captures the maximal amount of entanglement which can be distributed, if entanglement is quantified using the negativity. We analyze several channel models and demonstrate that, for various combinations of amplitude damping and depolarizing noise, entanglement distribution is only possible with weakly entangled input states. Excessive entanglement in the input state can hinder the channel's ability to establish entanglement. Our findings have implications for optimizing entanglement distribution in realistic quantum communication networks.
Quantum correlations between two or more different degrees of freedom of the same particle are sometimes referred to as intraparticle entanglement. In this work, we study these intraparticle correlations between two different degrees of freedom under various decoherence channels, viz. amplitude damping, depolarizing, and phase damping channels. We mainly focus on the amplitude-damping channel for which we obtain an exact analytical expression for the concurrence of an arbitrary initial pure state. In this channel, we observe the unique feature of entanglement arising from a separable initial state. We show that this channel allows for a revival of entanglement with an increasing damping parameter, including from a zero value of the concurrence. We also consider the amplitude-damping channel for interparticle entanglement and show that it does not display any of the above-mentioned interesting features. Further, for comparable parameters, the decay of entanglement in the interparticle system is much greater than in the intraparticle system, which we also find to be true for the phase damping and depolarizing channels. Thus, intraparticle entanglement subjected to damping is much more robust than interparticle entanglement.