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Journal of the Optical Society of America B

Entanglement synthesis based on the interference of a single-mode squeezed vacuum and a delocalized photon

Sergey A. Podoshvedov, Mikhail S. Podoshvedov

Published Mar 2, 2021• 13 citations
Publisher

Abstract

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.

DOI
10.1364/josab.415137

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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.
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 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 present a new method to entangle continuous variable (CV) states of certain parity and photonic states for the purpose of generating optical hybrid cluster (HC) states. To do it we introduce two families of the CV states of definite parity which stems from single mode squeezed vacuum (SMSV) state. Potential to apply the CV states of certain parity is high. We report on the generation of the even/odd Schrödinger cat state like (SCS-like) states whose fidelities with even/odd SCS of amplitude of [Formula: see text] are more of [Formula: see text], when 30,31 photons are detected in auxiliary mode of input SMSV state initially mixed with single photon. We show that the quantum efficiency of a photon number resolving (PNR) detector is crucial to maintaining the success rate of even/odd SCSs generator at an acceptable level. The scheme with delocalized photon implements deterministic imperfect entanglement operation between macro and micro states. We show that the beam splitter implements the two-qubits operation [Formula: see text] (CZ) for input CV states of definite parity and photonic states, provided that certain result is detected in measurement mode. An extension of the entangling operation for two entangled delocalized photons (TEDP) allows one to realize three-qubit HC state. Seven-qubit HC state is the result of conjunction of two three-qubit HC states through TEDP state.
We consider a family of continuous variable (CV) states being a superposition of displaced number states with equal modulo but opposite in sign displacement amplitudes. Either an even or odd CV state is mixed with a delocalized photon at a beam splitter with arbitrary transmittance and reflectance coefficients with the subsequent registration of the measurement outcome in an auxiliary mode to deterministically generate hybrid entanglement. We show that at certain values of the experimental parameters maximally entangled states are generated. The considered approach is also applicable to truncated finite versions of even/odd CV states. We study the nonclassical properties of the introduced states and show their Wigner functions exhibit properties inherent to nonclassical states. Other nonclassical properties of the states under consideration have also been studied.
We explore a scheme based on adding a nonlocal photon and subtracting some number of photons to entangle the initial single-mode squeezed vacuum (SMSV) state with the photon state. In a realistic model of interaction of the SMSV state with the photonic state on a beam splitter (BS) with changeable transmissivity or reflectivity the hybrid entanglement is realized for any values of the squeezing of input SMSV state. Maximum hybrid entanglement is achieved at certain values of the squeezing and BS parameter, which can mean implementation of a two-qubit controlled-Z (CZ-) operation using the BS with the appropriate initialization of the input states. The success probability of the gate, taking into account multiphoton outcomes in the measuring mode of the BS, is more than 0.3. We also propose to use new continuous variable (CV) states of definite parity that could increase the success probability of generating maximal hybrid entanglement. We show sufficient robustness of the generated entanglement under photon number resolving detection with practical quantum efficiency.
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).