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Journal of the Optical Society of America B

Bidirectional remote hyperstate preparation under common quantum control using hyperentanglement

Cao Thi Bich, Nguyen Ba An

Published Nov 14, 2022• 2 citations
Publisher

Abstract

In this paper, we propose a new, to the best of our knowledge, protocol that enables two distant parties to prepare a photon hyperstate for each other encoded at the same time in both polarization and spatial-mode degrees of freedom. The bidirectional remote hyperstate preparation is demanded so that it is remotely controllable by a common supervisor. Such a task appears possible using a shared quantum channel made of five photons entangled simultaneously in the two corresponding degrees of freedom, the so-called hyperentanglement. We first design a near-deterministic scheme to produce a relevant five-photon hyperentanagled state to be served as the working nonlocal channel and then present our protocol for controlled bidirectional remote hyperstate preparation, which always is successful.

DOI
10.1364/josab.471680

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In this paper, we propose a new, to the best of our knowledge, protocol that enables two distant parties to prepare a photon hyperstate for each other encoded at the same time in both polarization and spatial-mode degrees of freedom. The bidirectional remote hyperstate preparation is demanded so that it is remotely controllable by a common supervisor. Such a task appears possible using a shared quantum channel made of five photons entangled simultaneously in the two corresponding degrees of freedom, the so-called hyperentanglement. We first design a near-deterministic scheme to produce a relevant five-photon hyperentanagled state to be served as the working nonlocal channel and then present our protocol for controlled bidirectional remote hyperstate preparation, which always is successful.
Preparing quantum state remotely plays an important role in quantum communication network. Most of the previous protocols for parallel preparation quantum state remotely only consider parallel remote preparation of arbitrary single-qubit states. In this paper, we propose a protocol for parallel remote preparation of two-qubit hybrid states with a two-photon hyperentangled state. The arbitrary two-qubit hybrid states encoded in spatial-mode, frequency, polarization and time-bin degrees of freedom(DOFs) can be remotely prepared via hyperentangled state and optical elements. Moreover, we discuss parallel remote preparation of two-qubit hybrid states via partially hyperentangled state. The protocol for parallel remote preparation of two-qubit hybrid states has the advantage of having high channel capacity for long distance quantum communication by using hyperentangled state simultaneously entangled in spatial-mode, frequency, polarization and time-bin DOFs as the quantum channel.
Quantum remote control, also known as quantum remote implementation of an operator (QRIO), enables the remote manipulation of an arbitrary quantum state by implementing a desired quantum operation at a distant location. Significant progress has recently been made in developing QRIO protocols and their variants. Most existing schemes employ hyperentangled states where entanglement is shared across multiple degrees of freedom (DOFs). However, these protocols typically exploit only one degree of freedom at a time. In this work, we propose a QRIO protocol that simultaneously utilizes the polarization and spatial DOFs of a two-qubit hyperentangled state to remotely implement an arbitrary hybrid operator on an unknown single-photon two-qubit hyperstate. The shared hyperentangled resource is realized using the polarization and spatial modes of photons, while the protocol is constructed using linear optical elements and cross-Kerr nonlinear interactions to facilitate effective photon-photon coupling. Furthermore, the effects of measurement errors arising from finite coherent state distinguishability and coherent state dissipation are analyzed and the corresponding success probability of the protocol is evaluated. The results demonstrate that an appropriate choice of the cross-Kerr phase shift and coherent state amplitude significantly enhances the protocol performance, making the proposed scheme a promising candidate for hybrid quantum communication and distributed quantum information processing.
Abstract We propose a deterministic protocol for three distant parties to cooperate so that two parties can implement their secret unitary operators on the third party’s secret quantum state via shared quantum channel assisted by cross-Kerr nonlinearities. The operators are of general form while the state may be encoded either in spatial degree of freedom or polarization degree of freedom. The quantum channel is served by a three-photon hyperentangled state establishing the minimum of consumed photon number for this type of task. This protocol can be named joint remote implementation of operators which is necessary for distributed quantum tasks throughout a quantum network.
Abstract Hyper-entanglement is gaining more and more attentions thanks to its outstanding applications in processing quantum information. It is considered as a quantum resource in many important tasks. In this work, we deal with a tripartite task for three remote parties Alice, Bob and Charlie. Namely, Alice and Bob are two senders who independently share the full information of an arbitrary single-photon state which is encoded simultaneously in two different degrees of freedom, the spatial-mode degree of freedom and the polarization degree of freedom (hereafter called photon’s hyper-state). We show that Alice and Bob can jointly prepare for the receiver Charlie such a hyper-state of the photon when they share beforehand two pairs of hyper-Bell states.
Remote implementation of quantum operation between two distant nodes is crucial for many quantum applications. Here we consider the implementation of an arbitrary single-photon operation upon a remote quantum system exploiting photon pairs simultaneously entangled in the polarization and temporal degrees of freedom, which is a fascinating resource in long-distance quantum communication with its outstanding merits. To improve the level of security for the above protocol, we also consider a controlled implementation of quantum operation scenario by adding a supervisor, which is necessary for distributed quantum computation in a quantum network. Both of the protocols can be fulfilled by bidirectional state teleportation with the aid of the effective cross-Kerr interaction. Furthermore, the simple construction circuits together with available existing optical elements and common single-photon detectors facilitate the realization of our protocols with current sufficient technologies.
Abstract We present two schemes for asymmetric controlled bidirectional remote state preparation (CBRSP) with real and complex coefficients via seven- and ten-qubit entangled states, respectively, as the quantum channel. In these schemes, two distant parties—Alice and Bob—are not only senders but also receivers: Alice wants to remotely prepare a single-qubit state at Bob’s site; at the same time, Bob wishes to help Alice remotely prepare a two-qubit state. It is shown that the asymmetric CBRSP be can be completed successfully only if the two senders and the controller collaborate with each other. We demonstrate that, in our schemes, the total success probability of the asymmetric CBRSP can reach 1, that is, the schemes are deterministic.