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Physical Review A

Displaced photon states as resource for dense coding

Sergey A. Podoshvedov

Published Jan 20, 2009• 11 citations
Publisher

Abstract

We extend the analysis of dense coding protocol based on displaced photon states. The phase transformations with a displaced qubit allow for someone to transform five states to each other. Each ``particle-carrier'' (displaced qubit) carries an equal number of photons. On the receiving side, it is possible to decode all five outcomes using a linear optical scheme with beam splitters and on-off photodetectors that cannot discriminate different number of detected photons. Summarizing, interacting with only a single displaced qubit, it is possible to transmit two bits of information more. Optimal conditions to guarantee maximal communication rate ${\mathrm{log}}_{2}5$ per ``particle-carrier'' (displaced qubit) and influence of decoherence on the communication rate are considered.

DOI
10.1103/physreva.79.012319

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We extend the analysis of dense coding protocol based on displaced photon states. The phase transformations with a displaced qubit allow for someone to transform five states to each other. Each particle-carrier'' (displaced qubit) carries an equal number of photons. On the receiving side, it is possible to decode all five outcomes using a linear optical scheme with beam splitters and on-off photodetectors that cannot discriminate different number of detected photons. Summarizing, interacting with only a single displaced qubit, it is possible to transmit two bits of information more. Optimal conditions to guarantee maximal communication rate ${\mathrm{log}}_{2}5$ per particle-carrier'' (displaced qubit) and influence of decoherence on the communication rate are considered.
We propose an optical scheme to perform a complete Bell-state measurement of four entangled displaced states. The principal feature of the scheme is the use of the phase of the displaced photon. The main ingredients of the scheme are the resources of single photons, coherent radiation, and optical linear elements (beam splitters, phase-shifting devices). The optical scheme works with on-off photodetectors that cannot discriminate different numbers of detected photons. This type of measurement is adjusted for dense coding and a communication rate per photon is calculated for one partial case.
Theory of controlled tripartite quantum dense coding for the transmission of four-binary bits between two distinct locations is presented. The entanglement resource for this transmission is provided by a six-qubit cluster state. Theoretical detail of an encoder that can encode sixteen different operations and a four-bit binary decoder required for this transmission is discussed. We show that in the absence of availability of any four-state analyzer decoding can be reduced to single-particle and two-particle Bell-state measurements ( BSM ). In our scheme, Bell-state measurements ( BSM ) performed during decoding, result in Bell-pairs, which along with single-particle projections are used to unambiguously discriminate all sixteen encoding operations. Proposed experiment to verify theory of tripartite quantum dense coding scheme, using photonic entanglement, is also briefly discussed. Success probability of the scheme is determined. In addition, long-distance implementation of this tripartite quantum dense coding scheme is discussed. Fault-tolerant quantum repeaters used in this long-distance scheme are based on quantum errorcorrection, which is achieved with the aid of Calderbank-Shor-Steane ( CSS ) encoding.
Controlled dense coding which uses different five-qubit entangled systems is described in this article. Using a criterion based on quantum-statistical correlations to define the extent of entanglement, five-qubit states are shown to have genuine entanglement. Different schemes which are easily implementable experimentally for a receiver to decode the message from a sender are described. The importance of representation of a quantum channel and distribution of qubits in a communication protocol are emphasized. It is observed that when a controller is involved it is desirable that measurement results are transmitted to the receiver and not to the sender for experimental convenience. In addition, a controlled dense coding protocol for average information transfer is given for arbitrary (2N + 1)-qubit entangled systems, using the above schemes.
A novel scheme for realizing dense coding with Greenberger-Home-Zeilinger(GHZ) state in linear optical system is proposed.In this protocol,Alice codes on photon 1 and 2 by linear optical element and sents these photons to Bob.Then Bob performs a joint measurement on photons 1,2,and 3 with the GHZ basis by employing two quantum nondemolition detectors(QND) and polarizing beam splitter(PBS).Eight GHZ states can be completely discriminated.According to the outcomes of his measurement,Bob can determine what operation Alice applied.Alice only transmits two photons in this process of the quantum dense coding,but Bob can obtain three bits of classical information.The QND devices are generally based on cross-Kerr nonlinearities,and the cross-Kerr nonlinearities are available with electromagnetically induced transparency(EIT).
We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed form expression of the dense coding capacity for the cases of two and three senders that involve sharing of three- and four-mode states, respectively. The dense coding capacity is computed with the constraint of fixed average energy transmission when the modes of the sender are transferred to the receiver after the encoding operation. In both the cases, we demonstrate the quantum advantage of the protocol using paradigmatic classes of three- and four-mode states. The quantum advantage increases with the increase in the amount of energy that is allowed to be transmitted from the senders to the receiver.
Dense coding is a new concept of quantum communication using the nonlocal feature of quantum entangled states. Bob, the information receiver, prepares polarization-entangled photon twins and sends one of them to Alice, the information sender, while retaining the other. She can prepare each of the four Bell states by operating an appropriate manipulation only on the transmitted photon and thus she can encode 2 bits of information. To decode the 2 bits, Bob must execute a joint measurement of the returned and retained photons with a Bell-state analyzer, such as a Hong-Ou-Mandel type of two-photon interferometer. The information capacity of the transmitted photon is limited by the number of usable nonlocal quantum states which can be prepared through the local operation on one photon. A question arises as to whether Alice can enhance the capacity or not, by adopting an additional degree of freedom by use of pulse position modulation or optical frequency modulation for the transmitted photon. At a glance, capacity enhancement appears to be possible by introducing another degree of freedom. The question here is, however, whether or not it is possible by manipulating only one of photon twins. In the paper, however, we show that the information capacity in dense coding can be enhanced from the reported 2 bits to 3 bits provided that photon twins have spectral correlation and a perfect Bell state analyzer is available.