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arXiv:0909.0946 · Physical Review A

Coherent-state control of noninteracting quantum entanglement

Muhammed Yönaç, Joseph H. Eberly

Published Aug 19, 2010• 29 citations
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Abstract

We exploit a novel approximation scheme to obtain a new and compact formula for the parameters underlying coherent-state control of the evolution of a pair of entangled two-level systems. It is appropriate for long times and for relatively strong external quantum control via coherent-state irradiation. We take account of both discrete-state and continuous-variable degrees of freedom. The formula predicts the relative heights of entanglement revivals and their timing and duration.

DOI
10.1103/physreva.82.022321

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We exploit a novel approximation scheme to obtain a new and compact formula for the parameters underlying coherent-state control of the evolution of a pair of entangled two-level systems. It is appropriate for long times and for relatively strong external quantum control via coherent-state irradiation. We take account of both discrete-state and continuous-variable degrees of freedom. The formula predicts the relative heights of entanglement revivals and their timing and duration.
How to analytically deal with the entanglement and coherence dynamics of separated Jaynes–Cummings nodes with continuous-variable fields is still an open question. We here generalize this model to a more common situation including either a small or large qubit-field detuning, and obtain two new analytical formulas. The X-state simplification, Fock-state shortcut and detuning-limit approximation work together in an amazingly accurate way, which agrees with the numerical results. The new formulas almost perfectly predict the two-qubit entanglement dynamics both in sudden death and rebirth phenomenon for detuning interactions. We find that when both the qubit-field detuning and amplitude of coherent states are large enough, the maximal entanglement and coherence peaks can be fully and periodically retrieved, and their revival periods both increase linearly with the increasing detuning.
We present a hybrid quantum repeater protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable ddd-level systems, each of, in principle, arbitrary dimension ddd, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially efficient continuous-variable homodyne detections (``hybrid'' here refers to the simultaneous exploitation of discrete- and continuous-variable degrees of freedom for the local processing and storage of entangled states as well as their nonlocal distribution, respectively) and unambiguous state discrimination. For qutrits we quantify the light-matter entanglement that can be effectively shared through an elementary lossy channel, and for a repeater spacing of up to 10 km we show that the realistic (lossy) qutrit entanglement is even larger than any ideal (loss-free) qubit entanglement. After including qudit entanglement purification and swapping procedures, we calculate the long-distance entangled-pair distribution rates and the final entangled-state fidelities for total communication distances of up to 1280 km. For example, employing unambiguous state discrimination, with three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at an ideal maximal rate (assuming perfect gate operations) on the order of 100 Hz.
Quantum entanglement is the key property that makes quantum information theory different from its classical counterpart and is also a valuable physical resource with massive potential for technological applications. However, our understanding of entanglement is still far from complete despite intense research activities. Like other physical resources, the first step towards exploiting them fully is to know how to quantify. There are many reasons to focus on the entanglement of continuous-variable states since the underlying degrees of freedom of physical systems carrying quantum information are frequently continuous, rather than discrete. Much of the effort has been concentrated on Gaussian states, because these are common as the ground or \nthermal states of optical modes. Within this framework, many interesting topics have been studied and some significant progress made. Nevertheless, non-Gaussian states are also extremely important; this is especially so in condensed-phase systems, where harmonic behaviour in any \ndegree of freedom is likely to be only an approximation. So far, there is little knowledge about the quantification of entanglement in non-Gaussian states. \nThis thesis aims to contribute to the active field of research in quantum entanglement by introducing a new approach to the analysis of entanglement, especially in continuous-variable states, and shows that it leads to the first systematic quantification of the (local) entanglement \nin arbitrary bipartite non-Gaussian states. By applying this local approach, many new insights can be gained. Notably, local entanglements of systems with smooth wavefunctions are fully characterised by the derived simple expressions, provided the wavefunction is known. The local (logarithmic) negativity of any two-mode mixed states can be directly computed from the closed-form formulae given. For multi-mode mixed states, this approach provides a scheme that \npermits much simpler numerical computation for quantifying entanglement than is generally possible from directly computing the full entanglement of the system.