Recently, Li and Nie (Int. J. Theo. Phys. 52:1630, 2013) had introduced a bidirectional controlled quantum teleportation (BCQT) protocol by using GHZ-Bell state as a quantum channel. Also, Shukla et al. (Int. J. Theo. Phys. 52:3790, 2013) had shown the Li and Nie (LN) protocol is not a BCQT scheme. In this paper, two kinds of bidirectional teleportation schemes in order to correct and improve LN protocol are presented. In the first scheme, Alice and Bob as two legitimate users can simultaneously teleport an unknown single-qubit state to each other with the help of controller Charlie. In the second scheme, Alice can transmit two-qubit entangled state to Bob and at the same time Bob can teleport single-qubit state to Alice. In both of proposed schemes the quantum channel linking users is a GHZ-Bell state.
Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two quantum nodes. All bidirectional quantum teleportation protocols till now have achieved a maximum efficiency of $40\%$. Here, we propose a new scheme for symmetric bidirectional quantum teleportation using a six-qubit cluster state as the quantum channel, for symmetric ($3\leftrightarrow3$) qubit bidirectional quantum teleportation of a special three-qubit entangled state. The novelty of our scheme lies in its generalization for ($N\leftrightarrow N$) qubit bidirectional quantum telepor…
Recently, Ri-Gui Zhou et al. [Int. J. Theor. Phys. 59, 166-172 (2020)] proposed a scheme for bidirectional quantum teleportation of two-two and two-three qubit states by utilizing a six-qubit entangled state as a quantum channel. It is observed that the intrinsic efficiency calculated by Zhou et al. is not correct. In this improved scheme, we show that bidirectional teleportation of two-two and two-three qubit quantum states can be done by using optimized quantum resource and less consumption of classical resource. We also calculate the intrinsic efficiency of our improved scheme which is much…
In this paper, a bidirectional quantum teleportation protocol based on Einstein-Podolsky-Rosen (EPR) pairs and entanglement swapping is proposed. In this scheme, two users can simultaneously transmit an unknown single-qubit state to each other. The implementation of the proposed scheme is easier in experiment as compared to previous work. By utilizing this bidirectional quantum teleportation protocol, a bidirectional quantum secure direct communication scheme without carrying secret message is presented. Therefore, in the case of using perfect quantum channel, the protocol is completely secure…
A theoretical scheme for bidirectional swapping quantum controlled teleportation is presented using the entanglement property of maximally entangled five-qubit state, i.e., Alice wants to transmit a entangled state of particle a to Bob and Bob wants to transmit a entangled state of particle b to Alice via the control of the supervisor Charlie.
Bidirectional quantum teleportation scheme is a two-way quantum communication process, in which two parties simultaneously receive each other information. Recently, in paper [1] (Zhou et al., IEEE Access, 7, 44269 (2019)), a six-qubit cluster state has been used to teleport three-qubit entangled state (Alice) and arbitrary single-qubit unknown quantum state (Bob) bidirectionally. An experimental point of view, the preparation and the maintenance of cluster type entangled state is very difficult and costly. So, in this paper we have designed an optimal scheme for bidirectional quantum teleporta…
Recently bidirectional controlled perfect teleportation using 5-qubit states are reported in (Int. J. Theor. Phys. (2013) DOI 10.1007/s10773-013-1484-8 and ibid, (2013) DOI 10.1007/s10773-012-1208-5). In this paper we have shown that there exists a class of 5-qubit quantum states that can be used for bidirectional controlled teleportation. Two out of the three reported cases are the special cases of the proposed class of 5-qubit quantum states and one of them is not strictly a case of controlled bidirectional quantum teleportation. Further, we have shown that one can in principle, construct in…
In the present paper, a novel bidirectional quantum teleportation protocol is proposed. By using entanglement swapping technique, two GHZ states are shared as a quantum channel between Alice and Bob as legitimate users. In this scheme, based on control-not operation, single-qubit measurement and appropriate unitary operations, two users can simultaneously transmit a pure EPR state to each other. While, in the previous protocols, the users can just teleport a single-qubit state to each other via more than four-qubit state. Therefore, the proposed scheme is economical compared with previous prot…
Bidirectional quantum teleportation using quantum walks
Department of Physics, Government Arts and Science College, Meenchanda, Calicut, Kerala 673018, India（政府文理科学院）；Department of Physics, Government College, Malappuram, Kerala 676509, India（政府学院）
Relations between teleportation, Bell's inequalities and inseparability are investigated. It is shown that any mixed two spin-$1\over2$ state which violates the Bell-CHSH inequality is useful for teleportation. The result is extended to any Bell's inequalities constructed of the expectation values of products of spin operators. It is also shown that there exist inseparable states which are not useful for teleportation within the standard scheme.
In this paper, different from the other existing methods that only the special and limited numbers of qubits transmit between Alice and Bob, a general method is proposed to implement Bidirectional Quantum Controlled/uncontrolled Teleportation (BQCT/BQT) that Alice and Bob can transmit each type of arbitrary n and m-qubits to each other, simultaneously. This protocol is based on Controlled-NOT (CNOT) operation, appropriate single-qubit unitary operations and single-qubit measurement in the Z-basis and X-basis. Also, the quantum channel can be created by using Hadamard and CNOT operations. One o…
In this paper, a novel protocol for bidirectional controlled quantum teleportation (BCQT) is proposed. Based on entanglement swapping of initiate Bell state, two users can teleport an unknown single-qubit state to each other under the permission of the supervisor. This proposed protocol would be utilized to a system in which a controller controls the communication in one direction only. Indeed, just one of the users needs the permission of the controller to reconstruct the unknown quantum state. In comparison to the existing BCQT protocols which their quantum channels are cluster and brown sta…
We present a bidirectional modification of the standard one-qubit teleportation protocol, where both Alice and Bob transfer noisy versions of their qubit states to each other by using single Bell state and auxiliary (trigger) qubits. Three schemes are considered: the first where the actions of parties are governed by two independent quantum random triggers, the second with single random trigger, and the third as a mixture of the first two. We calculate the fidelities of teleportation for all schemes and find a condition on correlation between trigger qubits in the mixed scheme which allows us …
Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two parties. Specifically, the two individuals make use of a shared resource state as well as local operations and classical communication (LOCC) to swap quantum states. In this work, we concisely highlight the contributions of our companion paper [Siddiqui and Wilde, arXiv:2010.07905]. We develop two different ways of quantifying the error of nonideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity. We then establish that the values given …
A deterministic teleportation scheme for unknown atomic states is proposed in cavity QED. The Bell state measurement is not needed in the teleportation process, and the success probability can reach 1.0. In addition, the current scheme is insensitive to the cavity decay and thermal field.
In this paper, we define the return operator, the cross product operator and the cross Bell bases. Using the cross Bell bases, we give a protocol of teleportation of arbitrary multipartite qubit entanglement, this scheme is a quite natural generalization of the BBCJPW scheme. We find that this teleportation, in fact, is essentially determined by the teleportation of every single unknown qubit state as in the original scheme of BBCJPW. The calculation in detail is given for the case of tripartite qubit.
We study optimal teleportation based on the Bell measurements. An explicit expression for the quantum channel associated with the optimal teleportation with an arbitrary mixed state resource is presented. The optimal transmission fidelity of the corresponding quantum channel is calculated and shown to be related to the fully entangled fraction of the quantum resource, rather than the singlet fraction as in the standard teleportation protocol.
The question of the measurements on the Bell states by making use of mode change (from mixed to pure) of one qubit is considered. Such a mode change cannot be taken advantage of for superluminal communication in teleportation, and it may define constraints on the size of the gates.
In this contribution, we reformulated the bidirectional teleportation protocol suggested in [7], by means of Bloch vectors as well as the local operations are represented by using Pauli operators. Analytical and numerical calculations for the teleported state and Fisher information are introduced. It is shown that both quantities depend on the initial state settings of the teleported qubits and their triggers. The Fidelities and the Fisher information of the bidirectionally teleported states are maximized when the qubit and its trigger are polarized in the same direction. The minimum values ar…
We investigate the teleportation of the bipartite entangled states through two equally noisy quantum channels, namely mixture of Bell states. There is a particular mixed state channel for which all pure entanglement in a known Schmidt basis remain entangled after teleportation and it happens till the channel state remains entangled. Werner state channel lacks both these features. The relation of these noisy channels with violation of Bell's inequality and 2-E inequality is studied.
We present a novel Bell-state analyzer for time-bin qubits allowing the detection of three out of four Bell-states with linear optics, only two detectors and no auxiliary photons. The theoretical success rate of this scheme is 50%. A teleportation experiment was performed to demonstrate its functionality. We also present a teleportation experiment with a fidelity larger than the cloning limit.
We present a Bell-state analyzer for time-bin qubits allowing the detection of three out of four Bell-states with linear optics, two detectors and no auxiliary photons. The theoretical success rate of this scheme is 50%. A teleportation experiment was performed to demonstrate its functionality. We also present a teleportation experiment with a Fidelity larger than the cloning limit of F=5/6.
Dynamics of disentanglement as measured by the tripartite negativity and Bell nonlocality as measured by the extent of violation of the multipartite Bell-type inequalities are investigated in this work. It is shown definitively that for the initial three-qubit Greenberger-Horne-Zeilinger (GHZ) or {\it W} class state preparation the Bell nonlocality suffers sudden death under the influence of thermal reservoirs. Moreover, all the Bell-nonlocal states are useful for nonclassical teleportation, while there are entangled states that do not violate any Bell-type inequalities, but still yield noncla…
In this letter we analyze the efficacy of the entangled output of Pati-Braunstein deletion machine [3] as a teleportation channel. We analyze the possibility of it violating the Bell's inequality. Interestingly we find that for all values of the input parameter$α$ the state does not violate the Bell's inequality but when used as a teleportation channel can give a fidelity higher than the classical optimum (i.e 2/3).
Recently, a large number of protocols for bidirectional controlled state teleportation (BCST) have been proposed using $n$-qubit entangled states ($n\in\{5,6,7\}$) as quantum channel. Here, we propose a general method of selecting multi-qubit $(n>4)$ quantum channels suitable for BCST and show that all the channels used in the existing protocols of BCST can be obtained using the proposed method. Further, it is shown that the quantum channels used in the existing protocols of BCST forms only a negligibly small subset of the set of all the quantum channels that can be constructed using the propo…
We report a quantum teleportation experiment in which nonlinear interactions are used for the Bell state measurements. The experimental results demonstrate the working principle of irreversibly teleporting an unknown arbitrary quantum state from one system to another distant system by disassembling into and then later reconstructing from purely classical information and nonclassical EPR correlations. The distinct feature of this experiment is that \emph{all} four Bell states can be distinguished in the Bell state measurement. Teleportation of a quantum state can thus occur with certainty in pr…
An efficient and economical scheme is proposed for the perfect quantum teleportation of n-qubit non-maximally entangled state of generalized Bell-type. A Bell state is used as the quantum channel in the proposed scheme. It is also shown that the controlled teleportation of this n-qubit state can be achieved by using a GHZ state or a GHZ-like state as quantum channel. The proposed schemes are economical because for the perfect and controlled teleportation of n-qubit non-maximally entangled state of generalized Bell-type we only need a Bell state and a tripartite entangled state respectively. It…
We demonstrate an experiment on entanglement swapping using an optimal Bell-state measurement capable of identifying two of the four Bell-states for polarization entangled photons, which is the optimum with linear optical elements. The two final photons belong to separately created paris. They are entangled after their original partner photons have been subjected to the Bell state measurement, whose outcome determines the type of entanglement of the final photon pair. The resulting violation of Bell's inequality in both cases confirms the success of the teleportation protocol.
We study the quantum controlled and probabilistic teleportation protocol via a four-cluster state (Front. Phys. (2017) 12: 120306). The protocol cannot achieve the goal that if the teleportation fails, it can be repeated without copies of the teleported state. And the reason is that all the information of the teleported state shifts to the receiver's particle after Bell measurement and the information cannot shift back to the sender without other entangled states. To realize the claimed goal, a new quantum controlled and probabilistic teleportation protocol using the same four-cluster state is…
This paper proposes a scheme for creating and storing quantum entanglement over long distances. Optical cavities that store this long-distance entanglement in atoms could then function as nodes of a quantum network, in which quantum information is teleported from cavity to cavity. The teleportation can be carried out unconditionally via measurements of all four Bell states, using a method of sequential elimination.
A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.
In this work, a novel protocol is proposed for bidirectional controlled quantum teleportation (BCQT) in which a quantum channel is used with the eight-qubit entangled state. Using the protocol, two users can teleport an arbitrary entangled state and a pure two-qubit state (QBS) to each other simultaneously under the permission of a third party in the role of controller. This protocol is based on the controlled-not operation, appropriate single-qubit (SIQ) UOs and SIQ measurements in the Z and X-basis. Reduction of the predictability of the controller's qubit (QB) by the eavesdropper and also, …
The Wigner representation of parametric down conversion in the Heisenberg picture is applied to the study of the Rome teleportation experiment. We investigate the physical meaning of the zeropoint inputs at the different areas of the experimental setup. In particular, we establish a quantitative relationship between the zeropoint sets of modes that are needed for the preparation of the quantum state to be teleported, the idle channels inside the one-photon polarization-momentum Bell-state analyser, and the possibility of performing teleportation of a polarization state whith certainty.
In this paper we investigate the possibility to make complete Bell measurements on a product Hilbert space of two two-level bosonic systems. We restrict our tools to linear elements, like beam splitters and phase shifters, delay lines and electronically switched linear elements, photo-detectors, and auxiliary bosons. As a result we show that with these tools a never failing Bell measurement is impossible.
We analyze a possibility of using the two qubit output state from Buzek-Hillery quantum copying machine (not necessarily universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter $ξ$ for which the two qubit output state is entangled and violates Bell-CHSH inequality and for a different range it remains entangled but does not violate Bell-CHSH inequality. Further we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Bu…
Based on the assumption that the receiver Bob can apply any unitary transformation, Horodecki {\it et al.} [Phys. Lett. A {\bf 222}, 21 (1996)] proved that any mixed two spin-1/2 state which violates the Bell-CHSH inequality is useful for teleportation. Here, we further show that any X state which violates the Bell-CHSH inequality can also be used for nonclassical teleportation even if Bob can only perform the identity or the Pauli rotation operations. Moreover, we showed that the maximal difference between the two average fidelities achievable via Bob's arbitrary transformations and via the s…
Teleportation algorithm assumes specific Bell states as input, but actual sources typically generates more than one. This work presents a teleportation algorithm for a two Bell states mixture, including remaining distortion from previous control process.
A parametric amplifier is in essence a linear four-port device, which couples and linearly mixes two inputs before amplifying and sending them to two output ports. Here, we show that for quadrature-phase amplitudes, a parametric amplifier can replace beam splitters to play the role of mixer. We apply this idea to a continuous-variable quantum state teleportation scheme in which a parametric amplifier replaces a beam splitter in Bell measurement. We show that this scheme is loss-tolerant in the Bell measurement process and thus demonstrate the advantage of PA over BS in the applications in quan…
We introduce a general odd qubit entangled system composed of GHZ and Bell pairs and explicate its usefulness for quantum teleportation, information splitting and superdense coding. After demonstrating the superdense coding protocol on the five qubit system, we prove that '2N +1' classical bits can be sent by sending 'N+1' quantum bits using this channel. It is found that the five-qubit system is also ideal for arbitrary one qubit and two qubit teleportation and quantum information splitting (QIS). For the single qubit QIS, three different protocols are feasible, whereas for the two qubit QIS,…
We review and compare Bell-state measurement and quantum teleportation schemes using linear optics with three different types of resources, i.e., two-photon pairs, entangled coherent states and hybrid entangled states. Remarkably, perfect teleportation with linear optics is possible in principle based on a hybrid approach that combines two-photon pairs and entangled coherent states. It turns out that hybrid approach allows to perform Bell-state measurement and local Pauli operations in a deterministic way, while it requires photon number resolving measurements.
In a recent paper [Phys. Rev. A 70, 025803 (2004)] we presented a scheme to teleport an entanglement of zero- and one-photon states from a bimodal cavity to another one, with 100% success probability. Here, inspired on recent results in the literature, we have modified our previous proposal to teleport the same entangled state without using Bell-state measurements. For comparison, the time spent, the fidelity, and the success probability for this teleportation are considered.
The effect of non-orthogonality of an entangled non-orthogonal state based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single qubit state using all the Bell type entangled non-orthogonal states known as quasi Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi Bell state is optimal. Further, the perfo…
In this paper, we define a cross product operator and construct the cross Bell basis, by use this basis and Bell measurements we give a simple scheme of the teleportation of arbitrary multipartite qubit entanglement.
It is well-known that maximally entangled states such as the Greenberger-Horne-Zeilinger (GHZ) states, with the Bell states as the simplest examples, are widely exploited in quantum information and computation. We study the application of such maximally entangled states from the viewpoint of the GHZ transform, which is a unitary basis transformation from the product states to the GHZ states. The algebraic structure of the GHZ transform is made clear and representative examples for it are verified as multi-qubit Clifford gates. In this paper, we focus on the Bell transform as the simplest examp…
First, I show explicitly a scheme to {\it faithfully} and {\it deterministically} teleport an arbitrary 2-qubit state from Alice to Bob. In this scheme two same Bell states are sufficient for use. Bob can recover the 2-qubit state by performing at most 4 single-qubit unitary operations conditioned on Alice's 4-bit classical public message corresponding to her two Bell-state measurement outcomes. Then I generalize the 2-qubit teleportation scheme to an aribitrary $N(N\ge 3)$-qubit state teleportation case by using $N$ same Bell states. In the generalized scheme, Alice only needs to identify $N$…
The quantum teleportation process is composed of a joint measurement performed upon two subsystems A and B (uncorrelated), followed by a unitary transformation (parameters of which depend on the outcome of the measurement) performed upon a third subsystem C (EPR correlated with system B). The information about the outcome of the measurement is transferred by classical means. The measurement performed upon the systems A and B collapses their joint wavefunction into one of the four {\it entangled} Bell states. It is shown here that this measurement process plus a possible measurement on the thir…
In this contribution, we have investigated the bidirectional quantum teleportation (BQT) of single-qubit states using a Bell state influenced by decoherence channels with memory, dephasing and amplitude damping channels. The expressions of the negativity, as a measure of the entanglement remaining in the BQT quantum channel, the teleportation fidelities and the quantum Fisher information are also evaluated. We find that both these last quantities depend on the survival amount of entanglement in the BQT quantum channel, on the decoherence factor and on the correlation degree of the decoherence …
We suggest implementation of quantum teleportation protocol of unknown qubit beyond Bell states formalism. Hybrid entangled state composed of coherent components that belong to Alice and dual-rail single photon at Bob disposal is used. Nonlinear effect on the teleported state is realized due to peculiarity of interaction of coherent components with discrete variable state on a beam splitter. Bob performs unitary transformation after receiving the appropriate classical information. The protocol is nearly deterministic but the output state is subject to amplitude distortion which reduces the fid…
