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arXiv:1805.07519

Mechanism of interaction of discrete and continuous variable states for efficient generation of hybrid entangled states

Sergey A. Podoshvedov

Published May 19, 2018• 0 citations
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Abstract

We develop theory of realization of hybrid entanglement between discrete-variable (single photon) and continuous-variable states (coherent states). A highly transmissive beam splitter (HTBS) is used for interaction of the ingredients. Mechanism for generating the hybrid entangled states is based on the simultaneous displacement of the discrete-variable state on equal in absolute value but opposite in sign displacement amplitudes by coherent components, in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary mode. Conditions for the balanced hybrid entangled states generation are found. Our approach follows along lines experimentally demonstrated in Nat. Photonics 8, 570-574 (2014).

DOI
10.48550/arxiv.1805.07519

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We develop theory of realization of hybrid entanglement between discrete-variable (single photon) and continuous-variable states (coherent states). A highly transmissive beam splitter (HTBS) is used for interaction of the ingredients. Mechanism for generating the hybrid entangled states is based on the simultaneous displacement of the discrete-variable state on equal in absolute value but opposite in sign displacement amplitudes by coherent components, in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary mode. Conditions for the balanced hybrid entangled states generation are found. Our approach follows along lines experimentally demonstrated in Nat. Photonics 8, 570-574 (2014).
We propose a general approach for deterministic generation of the entangled hybrid states consisting of continuous variable (CV) and discrete variable (DV) states. Peculiarity of the interaction of DV and CV states on the beam splitter (BS) is key for the birth of the entangled hybridity provided that some measurement event is registered in auxiliary mode. We show that the CV states forming the output entangled state consist exclusively of either even or odd Fock states. Various input CV states, including the Schrödinger cat state, are tested at the input of the BS, where they mix with delocalized single photons. We show the hybrid entanglement generation is observed at arbitrary values of the experimental parameters used. The degree of the hybrid entanglement is evaluated. Conditions for generating the maximally entangled hybrid states are established.
We propose a new approach to the generation of entangled states, both hybrid and consisting exclusively of continuous variable (CV) states. A single mode squeezed vacuum is mixed with a delocalized single photon on arbitrary beam splitter (BS) with subsequent registration of some measurement outcome in auxiliary mode. The entangled states are generated whenever any event is measured in auxiliary mode. Negativity is used as a measure of entanglement. Under certain initial set conditions, the conditioned state becomes as entangled as possible. New types of CV states are introduced. This approach can be expanded to implement a high complexity quantum network.
We propose a new approach to generate entangled states, both hybrid and consisting exclusively of continuous variable (CV) states. A single-mode squeezed vacuum is mixed with a delocalized single photon on an arbitrary beam splitter with subsequent registration of measurement outcomes in auxiliary mode. The entangled hybrid states consisting of CV and discrete variable (DV) states are generated whenever any event is measured in auxiliary mode. Negativity is used as a measure of entanglement. Under certain initial conditions, the conditional state becomes as entangled as possible. New types of CV states, either even or odd depending on the parity of the Fock states forming the superpositions, are introduced. If the conditional entangled hybrid state is mixed with a single-mode squeezed vacuum with the subsequent registration of measurement results in DV mode, then the new state becomes CV entangled, i.e., its orthogonal components are already CV states. The entanglement synthesis can be expanded to implement a high-complexity quantum network.
Abstract Quantum teleportation of an unknown state basing on the interaction between discrete-valued states (DV) and continuous-valued states (CV) presented a particular challenge in quantum technologies. Here we consider the problem of controlled quantum teleportation of an amplitude-matched CV qubit, encoded by a coherent state of a varied phase as a superposition of the vacuum- and single-photon optical states among two distant partners Alice and Bob, with the consent of controller, Charlie. To achieve this task, we use an hybrid tripartite entangled state (interaction between the discrete and continuous variables states) as the quantum resource where the coherent part belongs to Alice, while the single-photon belongs to Bob and Charlie and the CV qubit is at the disposal of Alice. The discrete-continuous interaction is realized on highly transmissive beam-splitter. We have shown that the perfectly of teleportation fidelity depends on the phase difference between the phase of the state to teleport and the phase of the sender’s mode, we found that for a difference which approaches 0 or π , near perfect controlled quantum teleportation can be obtained in terms of the fidelity and independently of the amplitude α and the squeezing parameter ζ . Experimentally, this proposed scheme has been implemented using linear optical components such as beam splitter, phase shifters and photon counters.
We discuss some of the main features of a recently-generated form of hybrid entanglement between discrete- and continuous-variable states of light. Ideally, such a kind of entanglement should involve single-photon and coherent states as key representatives of the respective categories of states. Here we investigate the characteristics and limits of a scheme that, relying on a superposition of photon-creation operators onto two distinct modes, realizes the above ideal form of hybrid entanglement in an approximate way.
We propose a scheme to generate entanglement between a single-photon qubit in the polarization basis and a coherent state of light. The required resources are a superposition of coherent states, a polarization entangled photon pair, beam splitters, the displacement operation, and four photodetectors. Even when realistic detectors with a limited efficiency are used, an arbitrarily high fidelity can be obtained by adjusting a beam-splitter ratio and the displacement amplitude at the price of reducing the success probability. Our analysis shows that high fidelities may be obtained using on-off detectors with low efficiencies and available resource states under current technology.