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Chinese Physics B

Quantum superdense coding based on hyperentanglement

Ruitong Zhao, Qi Guo, Li Chen, Hong‐Fu Wang, Shou Zhang

Published Aug 1, 2012• 9 citations
Publisher

Abstract

We present a scheme for quantum superdense coding with hyperentanglement, in which the sender can transfer four bits of classical information by sending only one photon. The important device in the scheme is the hyperentangled Bell-state analyzer in both polarization and frequency degrees of freedom, which is also constructed in the paper by using a quantum nondemolition detector assisted by cross-Kerr nonlinearity. Our scheme can transfer more information with less resources than the existing schemes and is nearly deterministic and nondestructive.

DOI
10.1088/1674-1056/21/8/080303

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We present a scheme for quantum superdense coding with hyperentanglement, in which the sender can transfer four bits of classical information by sending only one photon. The important device in the scheme is the hyperentangled Bell-state analyzer in both polarization and frequency degrees of freedom, which is also constructed in the paper by using a quantum nondemolition detector assisted by cross-Kerr nonlinearity. Our scheme can transfer more information with less resources than the existing schemes and is nearly deterministic and nondestructive.
We present a scheme for quantum superdense coding with hyperentanglement,in which the sender can transfer four bits of classical information by sending only one photon.The important device in the scheme is the hyperentangled Bell-state analyzer in both polarization and frequency degrees of freedom,which is also constructed in the paper by using a quantum nondemolition detector assisted by cross-Kerr nonlinearity.Our scheme can transfer more information with less resources than the existing schemes and is nearly deterministic and nondestructive.
Hyperentanglement, the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention as it can be used to increase both the channel capacity of quantum communication and its security largely. Here, we present the first scheme to completely distinguish the hyperentangled Bell states of two-photon systems in three DOFs with the help of cross-Kerr nonlinearity without destruction, including two longitudinal momentum DOFs and the polarization DOF. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors which can be used to make a parity-check measurement and analyze Bell states of two-photon systems in different DOFs. Our complete scheme for two-photon six-qubit hyperentangled Bell-state analysis may be useful for the practical applications in quantum information, especially in long-distance high-capacity quantum communication.
A method of generating superdense coding based on quantum hyper-entanglement and facilitated by quantum networks is discussed. Superdense coding refers to the coding of more than one classical bit into each qubit. Quantum hyperentanglement refers to quantum entanglement in more than one degree of freedom, e.g. polarization, energy-time, and orbital angular momentum (OAM). The new superdense coding scheme permits 2L bits to be encoded into each qubit where L is the number of degrees of freedom used for quantum hyper-entanglement. The superdense coding procedure is based on a generalization of the Bell state for L degrees of freedom. Theory describing the structure, generation/transmission, and detection of the generalized Bell state is developed. Circuit models are provided describing the generation/transmission process and detection process. Detection processes are represented mathematically as projection operators. A mathematical proof that that the detection scheme permits the generalized Bell states to be distinguished with 100% probability is provided. Measures of effectiveness (MOEs) are derived for the superdense coding scheme based on open systems theory represented in terms of density operators. Noise and loss related to generation/transmission, detection and propagation are included. The MOEs include various probabilities, quantum Chernoff bound, a measure of the number of message photons that must be transmitted to successfully send and receive a message, SNR and the quantum Cramer Rao’ lower bound. Quantum networks with quantum memory are used to increase the efficiency of the superdense coding scheme.
Superdense coding (SDC) is a popular protocol demonstrating the potential of using quantum mechanics to transfer data, where The sender (Alice) can transfer 2 bits of classical information over a single qubit. We present a scheme for quantum superdense coding through Bragg diffracted hyperentangled atoms generated using cavity quantum electrodynamics (QED). In our scheme, Alice transfers 2 bits of classical information over a single hyperentangled atom. This is achieved by introducing multiple quantum gates using resonant and off-resonant Bragg diffraction in cavity QED setup. This scheme uses multiple degrees of freedom to add an extra layer of security to the encoded information.
We present a theoretical scheme for the complete Bell state measurement (BSM) for high-dimensional hyperentangled photons in polarization and path degrees of freedom (DOFs), in which the polarization entanglement is in two-dimensional Hilbert space and the path entanglement is in four-dimensional Hilbert space. This 2×4-dimensional photonic quantum system contains 64 mutually orthogonal high-dimensional hyperentangled Bell states, which can be unambiguously discriminated by using weak cross-Kerr nonlinearity, linear optical element, and single-photon detector. This is the first complete BSM scheme for high-dimensional hyperentangled photons in two DOFs assisted by the quantum nonlinear effect, and we also demonstrate its application in the quantum superdense coding protocol, which allows the transmission of log 2 64=6 bits of classical information via just sending one photon. Moreover, our scheme only requires the achievable small nonlinear phase shift, and it can provide new avenues for other BSM-based quantum information technologies involving photonic high-dimensional hyperentanglement.
Bell-state analysis (BSA) is essential in quantum communication, but it is impossible to distinguish unambiguously the four Bell states in the polarization degree of freedom (DOF) of two-photon systems with only linear optical elements, except for the case in which the BSA is assisted with hyperentangled states, the simultaneous entanglement in more than one DOF. Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell states in both the polarization and the spatial-mode DOFs of two-photon systems, by using the giant nonlinear optics in quantum dot-cavity systems. This scheme can be applied to increase the channel capacity of long-distance quantum communication based on hyperentanglement, such as entanglement swapping, teleportation, and superdense coding. We use hyperentanglement swapping as an example to show the application of this HBSA.