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Broadband teleportation and entanglement in cascaded open quantum systems

Changsuk Noh

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Quantum optics provides powerful means to probe quantum mechanics. In this \nthesis, we study various aspects of quantum phenomena arising in quantum optical \nsystems. Part I studies broadband quantum teleportation. After presenting three \ndifferent methods of analyzing the standard teleportation protocol, we study the \ninterplay between various bandwidths in determining the fidelity of a broadband \nquantum field teleportation. Explicit formulae for the degrees of first- and secondorder \ncoherence for the teleportation of resonance fluorescence are derived for this \npurpose. Part II studies entanglement arising in cascaded open quantum (optical) \nsystems. First, a detailed laser model is produced within quantum trajectory theory \nto study the total decoherence rate of a laser-driven qubit. Second, using this model, \nwe address the issue of laser quantum state, viewed in connection with separability \nof the laser-driven-qubit system. Third, a measure of entanglement within quantum \ntrajectory theory called ‘Contextual Entanglement’ is calculated for a few simple \nsystems and compared with the ‘Entanglement of Formation’. Lastly, we introduce \na method to quantify entanglement (based on the contextual entanglement) between \na source and the field it emits, which we call the ‘Entanglement Spectrum’. It is \napplied to study the entanglement between a laser-driven qubit and the field the \nqubit scatters.

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We develop a theoretical description of quantum wave mixing (QWM) in a cascaded waveguide-QED system of two superconducting qubits, where the probe is driven by an external coherent tone and by the resonance fluorescence of a strongly driven source qubit. Starting from the field correlation functions of the source emission, we derive an effective master-equation treatment for the probe and identify the regime in which the incident fluorescence is characterized by anomalous correlations. When the coherent Rayleigh component of the source spectrum is suppressed, the probe equations of motion become equivalent to those for a qubit driven by a coherent tone and broadband squeezed light, although the ligt emitted by the source is non-Gaussian and antibunched. This equivalence implies a selection rule for the peaks of the QWM spectrum, with a strong suppression of sidebands associated with processes involving an odd number of photons taken from the source field. Numerical simulations of the full cascaded two-qubit model for different ratios of radiative decay rates unambiguously confirm the participation of correlated photon pairs in QWM processes. The current research illustrates that the analysis of peak amplitudes can be used to probe photon statistics in the incident nonclassical field.

quant-pharXiv:2604.08139•Apr 10, 2026•0 citations
Quantum optics provides powerful means to probe quantum mechanics. In this \nthesis, we study various aspects of quantum phenomena arising in quantum optical \nsystems. Part I studies broadband quantum teleportation. After presenting three \ndifferent methods of analyzing the standard teleportation protocol, we study the \ninterplay between various bandwidths in determining the fidelity of a broadband \nquantum field teleportation. Explicit formulae for the degrees of first- and secondorder \ncoherence for the teleportation of resonance fluorescence are derived for this \npurpose. Part II studies entanglement arising in cascaded open quantum (optical) \nsystems. First, a detailed laser model is produced within quantum trajectory theory \nto study the total decoherence rate of a laser-driven qubit. Second, using this model, \nwe address the issue of laser quantum state, viewed in connection with separability \nof the laser-driven-qubit system. Third, a measure of entanglement within quantum \ntrajectory theory called ‘Contextual Entanglement’ is calculated for a few simple \nsystems and compared with the ‘Entanglement of Formation’. Lastly, we introduce \na method to quantify entanglement (based on the contextual entanglement) between \na source and the field it emits, which we call the ‘Entanglement Spectrum’. It is \napplied to study the entanglement between a laser-driven qubit and the field the \nqubit scatters.
Quantum teleportation of an unknown broadband electromagnetic field is investigated. The continuous-variable teleportation protocol by Braunstein and Kimble [Phys. Rev. Lett. 80, 869 (1998)] for teleporting the quantum state of a single mode of the electromagnetic field is generalized for the case of a multimode field with finite bandwith. We discuss criteria for continuous-variable teleportation with various sets of input states and apply them to the teleportation of broadband fields. We first consider as a set of input fields (from which an independent state preparer draws the inputs to be teleported) arbitrary pure Gaussian states with unknown coherent amplitude (squeezed or coherent states). This set of input states, further restricted to an alphabet of coherent states, was used in the experiment by Furusawa et al. [Science 282, 706 (1998)]. It requires unit-gain teleportation for optimizing the teleportation fidelity. In our broadband scheme, the excess noise added through unit-gain teleportation due to the finite degree of the squeezed-state entanglement is just twice the (entanglement) source's squeezing spectrum for its ``quiet quadrature.'' The teleportation of one half of an entangled state (two-mode squeezed vacuum state), i.e., ``entanglement swapping,'' and its verification are optimized under a certain nonunit gain condition. We will also give a broadband description of this continuous-variable entanglement swapping based on the single-mode scheme by van Loock and Braunstein [Phys. Rev. A 61, 10 302 (2000)].
We demonstrate an unconditional high-fidelity teleporter capable of preserving the broadband entanglement in an optical squeezed state. In particular, we teleport a squeezed state of light and observe -0.8+/-0.2 dB of squeezing in the teleported (output) state. We show that the squeezing criterion translates directly into a sufficient criterion for entanglement of the upper and lower sidebands of the optical field. Thus, this result demonstrates the first unconditional teleportation of broadband entanglement. Our teleporter achieves sufficiently high fidelity to allow the teleportation to be cascaded, enabling, in principle, the construction of deterministic non-Gaussian operations.
This dissertation consists of three sections. In the first section, we discuss the generation \nof arbitrary two-qubit entangled states and present three generation methods. \nThe first method is based on the interaction of an atom with classical and quantized \ncavity fields. The second method is based on the interaction of two coupled two-level \natoms with a laser field. In the last method, we use two spin-1/2 systems which \ninteract with a tuned radio frequency pulse. Using those methods we have generated \ntwo qubit arbitrary entangled states which is widely used in quantum computing and \nquantum information. In the second section, we discuss a possible experimental implementation \nof quantum walk which is based on the passage of an atom through a \nhigh-Q cavity. The chirality is determined by the atomic states and the displacement \nis characterized by the photon number inside the cavity. Our scheme makes quantum \nwalk possible in a cavity QED system and the results could be widely used on \nquantum computer. In the last section, we investigate the properties of teleporting \nan arbitrary superposition of entangled Dicke states of any number of atoms (qubits) \nbetween two distant cavities. We also studied teleporting continuous variables of an \noptical field. Teleportation of Dicke states relies on adiabatic passage using multiatom \ndark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate \nthe protocol of quantum teleportation of arbitrary input optical field states in \nthe density matrix form, and established the relation between the P-function of the \ninput and output states. We then present a condition involving squeeze parameter \nand detection efficiency under which the P-function of the output state becomes the \nQ function of the input state such that any nonclassical features in the input state \nwill be eliminated in the teleported state. Based on the research in this section we \nhave made it possible of arbitrary atomic Dicke states teleportation from one cavity \nto another, and this teleortation will play an essential role in quantum communication. \nSince quantum properties is so important in quantum communication, the \ncondition we give in this section to distinguish classical and quantum teleportation is \nalso important.
We review and compare Bell-state measurement and quantum teleportation schemes using linear optics with three different types of resources, i.e., two-photon pairs, entangled coherent states and hybrid entangled states. Remarkably, perfect teleportation with linear optics is possible in principle based on a hybrid approach that combines two-photon pairs and entangled coherent states. It turns out that hybrid approach allows to perform Bell-state measurement and local Pauli operations in a deterministic way, while it requires photon number resolving measurements.
The theory of open systems is used in quantum optics in two distinct ways: to model sources of light such as lasers and parametric oscillators, and to describe the response of irradiated cavities and atoms. Sometimes the two applications are used in combination; first, statistical properties of the field radiated by a source are calculated, and these are then used in a separate calculation to determine the response of a system that is irradiated by the source. But the usefulness of this approach is quite hunted. It is essentially limited to coherent sources and certain broadband sources such as broadband squeezed or chaotic light. There exists no general theory for cascaded open systems - a theory that gives the response of system B to radiation emitted by system A when there exists an open-systems treatment for A and B separately. In this paper I develop such a theory using the quantum trajectory formulation of open systems. The source A and irradiated system B are described by a single stochastic wave-function. Generally the wavefunction describes an entangled state of the A and B subsystems. In the quantum trajectory formalism the wavefunction undergoes a coherent evolution governed by a nonunitary Schrödinger equation, interrupted at random times by wavefunction collapses. I derive the nonunitary Schrödinger equation and the form of the collapses. I illustrate the theory with some simple examples and discuss potential applications to problems involving the interaction of atoms with nonclassical light.
We develop a theoretical description of quantum wave mixing (QWM) in a cascaded waveguide-QED system of two superconducting qubits, where the probe is driven by an external coherent tone and by the resonance fluorescence of a strongly driven source qubit. Starting from the field correlation functions of the source emission, we derive an effective master-equation treatment for the probe and identify the regime in which the incident fluorescence is characterized by anomalous correlations. When the coherent Rayleigh component of the source spectrum is suppressed, the probe equations of motion become equivalent to those for a qubit driven by a coherent tone and broadband squeezed light, although the ligt emitted by the source is non-Gaussian and antibunched. This equivalence implies a selection rule for the peaks of the QWM spectrum, with a strong suppression of sidebands associated with processes involving an odd number of photons taken from the source field. Numerical simulations of the full cascaded two-qubit model for different ratios of radiative decay rates unambiguously confirm the participation of correlated photon pairs in QWM processes. The current research illustrates that the analysis of peak amplitudes can be used to probe photon statistics in the incident nonclassical field.