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International Conference on Signal Processing and Advance Research in Computing (SPARC)

Quantum Tele-Amplification of Non-Gaussian State via bi-modal Asymmetric Entangled Coherent State

Ankita Pathak, Ravi Shankar Singh

Published Sep 12, 2024• 0 citations
Publisher

Abstract

Optical Coherent State (OCS), generated by LASERS, exhibits Gaussian probability (Wigner) distribution function with minimum uncertainty-spread in quantum phase space. It provides over-complete states spanning infinite dimensional Hilbert space, an emblematic instance of continuous variable states. Quantum superposition of Cat Coherent States (CCS), named as Schrodinger CCS due to historical reasons and visualized as non-Gaussian Wigner distribution function in phase space, furnishes quantum resources for quantum information science, engineering and technology i.e., quantum non-locality, quantum teleportation, and tele-amplification, to name a few. We proposed a protocol to teleporting mono-modal non-Gaussian OCS (Schrodinger CCS) conjoined with its amplification via asymmetric two mode entangled CCS as quantum channel. The fidelity and probability of successful event and unsuccessful event quantum tele-amplification is defined for various heralding conditions at sender’s lab. It is seen that the probability of faithful and unfaithful quantum tele-amplification is fifty percent with unit fidelity for intense OCS. Prospective utility of our scheme may overlong distances transmission where loss in photon is inevitable.

DOI
10.1109/sparc61891.2024.10828916

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Optical Coherent State (OCS), generated by LASERS, exhibits Gaussian probability (Wigner) distribution function with minimum uncertainty-spread in quantum phase space. It provides over-complete states spanning infinite dimensional Hilbert space, an emblematic instance of continuous variable states. Quantum superposition of Cat Coherent States (CCS), named as Schrodinger CCS due to historical reasons and visualized as non-Gaussian Wigner distribution function in phase space, furnishes quantum resources for quantum information science, engineering and technology i.e., quantum non-locality, quantum teleportation, and tele-amplification, to name a few. We proposed a protocol to teleporting mono-modal non-Gaussian OCS (Schrodinger CCS) conjoined with its amplification via asymmetric two mode entangled CCS as quantum channel. The fidelity and probability of successful event and unsuccessful event quantum tele-amplification is defined for various heralding conditions at sender’s lab. It is seen that the probability of faithful and unfaithful quantum tele-amplification is fifty percent with unit fidelity for intense OCS. Prospective utility of our scheme may overlong distances transmission where loss in photon is inevitable.
Optical coherent states are experimentally realizable continuous variable quantum states of which preparation by lasers, as well as its manipulation and monitoring by linear optical gadgets are well established. We propose a strategy to send an arbitrary superposition of four-component bimodal entangled coherent states from a sender to a receiver who, simultaneously, tries to transmit an unknown Schrodinger Cat coherent state to sender via employing a cluster consisting of three superposition of two component bimodal entangled coherent states as the quantum channel and utilizing linear optical gadgets. Heralded detection of photons in laboratories of sender and receiver followed by classical communications of even and odd number of photons and local unitary operations, impeccably, accomplishes simultaneous faithful asymmetric bidirectional quantum teleportation with one eighth of probability of success. It is seen that not all detection events implement the protocol and, therefore, one has to locally apply displacement operator, a necessary evil. We analyze near faithful partial asymmetric bidirectional quantum teleportation and associated probability of success therein. We demonstrated that, for an intense coherent optical field, fidelity approach unity.
In continuous-variable quantum information, non-Gaussian entangled states that are obtained from Gaussian entangled states via photon subtraction are known to contain more entanglement. This makes them better resources for quantum information processing protocols, such as, quantum teleportation. We discuss the teleportation of non-Gaussian, non-classical Schrödinger-cat states of light using two-mode squeezed vacuum light that is made non-Gaussian via subtraction of a photon from each of the two modes. We consider the experimentally realizable cat states produced by subtracting a photon from the single-mode squeezed vacuum state. We discuss two figures of merit for the teleportation process, (a) the fidelity, and (b) the maximum negativity of the Wigner function at the output. We elucidate how the non-Gaussian entangled resource lowers the requirements on the amount of squeezing necessary to achieve any given fidelity of teleportation, or to achieve negative values of the Wigner function at the output.
Glauber's coherent state is denoted by ∣α⟩\ketα∣α⟩ and its two-mode extension is represented by ∣α,β⟩\ket{α,β}∣α,β⟩. In this work, we introduce a two-mode superposition operator A=tab+ra†b†A=tab+ra^\dagger b^\daggerA=tab+ra†b†, whose action on the two-mode coherent state produces the two-mode coherent superposed quantum state ∣ψ⟩=(tab+ra†b†)∣α,β⟩\ketψ=(tab+ra^\dagger b^\dagger)\ket{α,β}∣ψ⟩=(tab+ra†b†)∣α,β⟩. We investigate the nonclassicality and quantum non-Gaussianity of this state by means of the Wigner distribution and Wigner logarithmic negativity. Once its intrinsic nonclassical and non-Gaussian structure is established, the state is employed as the entangled resource in the Braunstein-Kimble continuous-variable (CV) teleportation protocol. We compute the ideal teleportation fidelity for coherent and squeezed inputs and analyze how the strengths of nonclassicality and non-Gaussianity influence the teleportation efficiency. Our results identify specific parameter regimes where enhanced non-Gaussian features or increased nonclassicality enable fidelities beyond the classical threshold, thereby revealing the operational significance of engineered two-mode quantum states in CV quantum information processing.
Entangled coherent states (ECS) provide a powerful non-Gaussian resource for continuous-variable quantum communication, but their generation in scalable architectures remains challenging. We propose an integrated photonic scheme that creates high-fidelity ECS from a two-mode squeezed vacuum via photon subtraction in a symmetric waveguide trimer. The resulting non-Gaussian entanglement is further enhanced by single-photon catalysis, which purifies the distributed state after transmission through lossy channels. Using these purified ECS resources, we analyze a photon-number-based teleportation protocol and demonstrate high-fidelity transfer of both coherent states and Schrodinger cat states. In particular, the teleportation fidelity for cat states exceeds the classical threshold of 2/3 over a broad range of realistic channel and squeezing parameters, whereas Gaussian resources fail to do so. Our results show that integrated photon subtraction and catalysis enable practical, chip-compatible generation of non-Gaussian entanglement suitable for advanced quantum teleportation and continuous-variable quantum networks.
Quantum teleportation enables transferring quantum states by leveraging entanglement. The distribution of entangled states is challenged by decoherence, which degrades the teleportation performance. Continuous-variable teleportation with coherent-state qubits has gained particular interest because it can provide better performance than discrete-variable teleportation with polarization-encoded qubits and is more resilient to decoherence. However, most existing schemes employ a specific configuration of coherent-state qubits, namely Schrödinger cat states, and assume symmetric photon-loss channels. This work explores the teleportation of qubits based on coherent states through asymmetric quantum channels impaired by photon loss. First, we characterize the teleportation protocol for arbitrary coherent-state qubit configurations considering asymmetric and photon-loss channels. Then, we present case studies under both ideal entanglement distribution and lossy conditions. Results reveal a trade-off between state distinguishability and teleportation fidelity, providing insight into the optimal design of coherent-state qubits in practical teleportation protocols.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrodinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).