We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality $d$. We consider four classes of noise: dit-flip, $d$-phase-flip, dit-phase-flip and depolarizing, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension $d$ for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the $d$-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviours and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis by Fortes and Rigolin for the case of qubits (Phys. Rev. A, 92 012338, 2015).
Entanglement is a key resource in many quantum information applications. One of these applications is quantum teleportation.The purpose of teleportation is sending qubits across quantum channels. In general these quantum channels are noisy and therefore limit the fidelity of transmission.In this paper we consider the effect of noise on teleportation and finally find the fidelity of teleportation in presence of noise.
We address continuous variable quantum teleportation in Gaussian quantum noisy channels, either thermal or squeezed-thermal. We first study the propagation of twin-beam and evaluate a threshold for its separability. We find that the threshold for purely thermal channels is always larger than for squeezed-thermal ones. On the other hand, we show that squeezing the channel improves teleportation of squeezed states and, in particular, we find the class of squeezed states that are better teleported in a given noisy channel. Finally, we find regimes where optimized teleportation of squeezed states …
Partial teleportation of entanglement is to teleport one particle of an entangled pair through a quantum channel. This is conceptually equivalent to quantum swapping. We consider the partial teleportation of entanglement in the noisy environment, employing the Werner-state representation of the noisy channel for the simplicity of calculation. To have the insight of the many-body teleportation, we introduce the measure of correlation information and study the transfer of the correlation information and entanglement. We find that the fidelity gets smaller as the initial-state is entangled more f…
The quantum teleportation with noisy EPR state is discussed. Using an optimal decomposition technique, we compute the concurrence, entanglement of formation and Groverian measure for various noisy EPR resources. It is shown analytically that all entanglement measures reduce to zero when $\bar{F} \leq 2/3$, where $\bar{F}$ is an average fidelity between Alice and Bob. This fact indicates that the entanglement is a genuine physical resource for the teleportation process. This fact gives valuable clues on the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompos…
We establish the optimal quantum teleportation protocol for the realistic scenario when both input state and quantum channel are afflicted by noise. In taking these effects into account higher fidelities are achieved. The optimality of the proposed protocol prevails even when restricted to a reduced set of generically available operations.
Authenticated teleportation aims to certify the transmission of a quantum state through teleportation, even in the presence of an adversary. This scenario can be pictured in terms of an untrusted source distributing a Bell state between two parties who wish to verify it using some simple tests. We propose a protocol that achieves this goal in a practical way, and analyse its performance and security when the parties have noisy measurement devices. Further, we model a realistic experimental scenario where the state is subject to noise and dephasing. We finally apply our analysis to the verifica…
Quantum teleportation requires the transmission of entangled pairs to Alice and Bob. Transmission errors modify the entangled state before the teleportation can be performed. We determine the changes in the output state caused by such transmission errors. It is shown that the errors caused by entanglement transmission are equivalent to the errors caused in a direct transmission of a quantum state from Alice to Bob.
Quantum teleportation enables deterministic and faithful transmission of quantum states, provided a maximally entangled state is pre-shared between sender and receiver, and a one-way classical channel is available. Here, we prove that these resources are not only sufficient, but also necessary, for deterministically and faithfully sending quantum states through any fixed noisy channel of maximal rank, when a single use of the cannel is admitted. In other words, for this family of channels, there are no other protocols, based on different (and possibly cheaper) sets of resources, capable of rep…
We constructed a class of non-maximally entangled mixed states \cite{roy2010} and extensively studied its entanglement properties and also their usefulness as teleportation channels. In this article, we revisited our constructed state and have studied it from three different perspectives. Since every entangled state is associated with an witness operator, we have found a suitable entanglement as well as teleportation witness for our non-maximally entangled mixed states. We considered the noisy channel's effects on our constructed state and to see whether it affects the states' capacity as tele…
We employ the technique of weak measurement in order to enable preservation of teleportation fidelity for two-qubit noisy channels. We consider one or both qubits of a maximally entangled state to undergo amplitude damping, and show that the application of weak measurement and a subsequent reverse operation could lead to a fidelity greater than $2/3$ for any value of the decoherence parameter. The success probability of the protocol decreases with the strength of weak measurement, and is lower when both the qubits are affected by decoherence. Finally, our protocol is shown to work for the Wern…
We investigate continuous variable (CV) quantum teleportation using relevant classes of non-Gaussian states of the radiation field as entangled resources. First, we introduce the class two-mode squeezed symmetric superposition of Fock states, including finite truncations of twin-beam Gaussian states as special realizations. These states depend on a set of free independent parameters that can be adjusted for the optimization of teleportation protocols, with an enhancement of the success probability of teleportation both for coherent and Fock input states. We show that the optimization procedure…
We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noise acting on quantum channels. If the quantum channels is subject to isotropic noise, the average fidelity decays to 1/2, which is smaller than the best possible value 2/3 obtained only by the classical communication. On the other hand, if…
We analyze the average fidelity (say, F) and the fidelity deviation (say, D) in noisy-channel quantum teleportation. Here, F represents how well teleportation is performed on average and D quantifies whether the teleportation is performed impartially on the given inputs, that is, the condition of universality. Our analysis results prove that the achievable maximum average fidelity ensures zero fidelity deviation, that is, perfect universality. This structural trait of teleportation is distinct from those of other limited-fidelity probabilistic quantum operations, for instance, universal-NOT or…
We report experimental results on the action of selected local environments on the fidelity of the quantum teleportation protocol, taking into account non-ideal, realistic entangled resources. Different working conditions are theoretically identified, where a noisy protocol can be made almost insensitive to further addition of noise. We put to test these conditions on a photonic implementation of the quantum teleportation algorithm, where two polarization entangled qubits act as the entangled resource and a path qubit on Alice encodes the state to be teleported. Bob's path qubit is used to imp…
We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for $n$-qubit GHZ states $n\in\{4,5,6\}$ where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity we show that 3GHZ state is more robust than $n$GHZ state u…
Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.} singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transfrom one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{Ψ^-}$)…
Transfer of entanglement and information is studied for quantum teleportation of an unknown entangled state through noisy quantum channels. We find that the quantum entanglement of the unknown state can be lost during the teleportation even when the channel is quantum correlated. We introduce a fundamental parameter of correlation information which dissipates linearly during the teleportation through the noisy channel. Analyzing the transfer of correlation information, we show that the purity of the initial state is important in determining the entanglement of the replica state.
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.
Recently Badziag \emph{et al.} \cite{badziag} obtained a class of noisy states whose teleportation fidelity can be enhanced by subjecting one of the qubits to dissipative interaction with the environment via amplitude damping channel (ADC). We show that such noisy states result while sharing the states (| Φ^{\pm}> =\frac{1}{\sqrt{2}}(| 00> \pm | 11>)) across ADC. We also show that under similar dissipative interactions different Bell states give rise to noisy entangled states that are qualitatively very different from each other in the sense, only the noisy entangled states constructed from th…
Quantum teleportation is one of the most pioneering features of the quantum world. Typically, the quality of a teleportation protocol is solely judged by its average fidelity. In this work, we analyze the performance of teleportation in terms of both fidelity and the deviation in fidelity. Specifically, we define a quantity called teleportability score, which incorporates contributions from both the fidelity and its deviation. It also takes into account the sensitivity one requires for a protocol in which the teleportation of a quantum state is required in one or many intermediate steps. We co…
In our work we consider the following problem in the context of teleportation: an unknown pure state have to be teleported and there are two laboratories which can perform the task. One laboratory uses a pure non maximally entangled channel but has a capability of performing the joint measurement on bases with a constrained degree of entanglement; the other lab makes use of a mixed X-state channel but can perform a joint measurement on bases with higher entanglement degrees. We compare the average teleportation fidelity achieved in both cases, finding that the fidelity achieved with the X-stat…
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, …
Quantum teleportation channels can overcome the effects of photonic loss, a major challenge in the implementation of a quantum network over fiber. Teleportation channels are created by distributing an entangled state between two nodes which is a probabilistic process requiring classical communication. This causes critical delays that can cause information loss as quantum data suffers from decoherence when stored in memory. In this work, we quantify the effect of decoherence on fidelity at a node in a quantum network due to the storage of qubits in noisy memory platforms. We model the memory pl…
Which state does lose less quantum information between GHZ and W states when they are prepared for two-party quantum teleportation through noisy channel? We address this issue by solving analytically a master equation in the Lindbald form with introducing the noisy channels which makes the quantum channels to be mixed states. It is found that the answer of the question is dependent on the type of the noisy channel. If, for example, the noisy channel is ($L_{2,x}$, $L_{3,x}$, $L_{4,x}$)-type where $L's$ denote the Lindbald operators, GHZ state is always more robust than W state, i.e. GHZ state …
Noisy teleportation of nonclassical quantum states via a two-mode squeezed-vacuum state is studied with the completely positive map and the Glauber-Sudarshan $P$-function. Using the nonclassical depth as a measure of transmission performance, we compare the teleportation scheme with the direct transmission through a noisy channel. The noise model is based on the coupling to the vacuum field. It is shown that the teleportation channel has better transmission performance than the direct transmission channel in a certain region. The bounds for such region and for obtaining the nonvanished nonclas…
We study the fidelity of quantum teleportation for the situation in which quantum logic gates are used to provide the long distance entanglement required in the protocol, and where the effect of a noisy environment is modeled by means of a generalized amplitude damping channel. Our results demonstrate the effectiveness of the quantum trajectories approach, which allows the simulation of open systems with a large number of qubits (up to 24). This shows that the method is suitable for modeling quantum information protocols in realistic environments.
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…
We study the activation of entanglement in teleportation protocols. To this end, we a present derivation of the average fidelity of teleportation process with noisy classical channel for qudits. In our work we do not make any assumptions about the entangled states shared by communicating parties. Our result allows us to specify the minimum amount of classical information required to beat the classical limit when the protocol is based on the Bell measurements. We also compare average fidelity of teleportation obtained using noisy and perfect classical channel with restricted capacity. The most …
The possibility of teleportation is by sure the most interesting consequence of quantum non-separability. So far, however, teleportation schemes have been formulated by use of state vectors and considering individual entities only. In the present article the feasibility of teleportation is examined on the basis of the rigorous ensemble interpretation of quantum mechanics (not to be confused with a mere treatment of noisy EPR pairs) leading to results which are unexpected from the usual point of view.
Non-commuting noises may give rise to entanglement sudden death. By considering the decoherence dynamics during establishment of the channel states and noisy recovery operations, we study further the impact of non-commuting noises on single- and two-qubit teleportation. We show that in the presence of these noises there exists a critical rate of recovery operation below which teleportation will fail.
Causal order can improve the quantum information transmission in teleportation due a noisy entangled resource by using an appropriate measurement state on the control state ruling the causal order. In this work, we get analytically the fidelity for the entire process under an arbitrary measurement over such control state and then we get a perfect teleportation by selecting the optimal measurement on it. We also analyse other values characterizing the imperfect entangled state where a perfect teleportation can not be reached. Notably, we determine that the best fidelity does not depend on the p…
We study quantum teleportation with the resource of non-orthogonal qubit states. We first extend the standard teleportation protocol to the case of such states. We investigate how the loss of teleportation fidelity resulting for the use of non-orthogonal states compares to a similar loss of fidelity when noisy or non-maximally entangled states as used as teleportation resource. Our analysis leads to certain interesting results on the teleportation efficiency of both pure and mixed non-orthgonal states compared to that of non-maximally entangled and mixed states.
The protocol of the teleportation of an arbitrary unknown one-qubit state is investigated when the quantum channel is subject to the decoherence from the non-Markovian environments with the memory effects. The quality of the teleportation measured by the average fidelity and minimal fidelity can be enhanced in the non-Markovian channel. The memory effects give rise to the revival of the fidelity which is better than that obtained by the Markovian channel.
By solving analytically a master equation in the Lindblad form, we study quantum teleportation of the one-qubit state under the influence of different surrounding environments, and compared the robustness between Greenberger-Horne-Zeilinger (GHZ) and W states in terms of their teleportation capacity. The results revealed that when subject to zero temperature environment, the GHZ state is always more robust than the W state, while the reverse situation occurs when the channel is subject to infinite temperature or dephasing environment.
The one-qubit teleportation protocol is reexamined when it is executed in the presence of various decohering environments. The results revealed that this quantum protocol is more robust under the influence of dephaisng environment than those under the influence of dissipative or noisy environment. The environment may deprive the quantum advantage of teleportation over purely classical communication in a finite or infinite lifetime, which is dependent on the type of environment. Also we found that except entanglement, the purity of the entangled state resource is also crucial in determine the q…
We have tried to interpret the physical role of the three-tangle and $π$-tangle in the real physical information process. For the model calculation we adopt the three-party teleportation scheme through the various noisy channels. The three parties consist of sender, accomplice and receiver. It is shown that the $π$-tangles for the X- and Z-noisy channels vanish at $κt \to \infty$ limit, where $κt$ is a parameter introduced in the master equation of Lindblad form. In this limit the receiver's maximum fidelity reduces to the classical limit 2/3. However, this nice feature is not maintained at th…
We show how an interaction with the environment can enhance fidelity of quantum teleportation. To this end, we present examples of states which cannot be made useful for teleportation by any local unitary transformations; nevertheless, after being subjected to a dissipative interaction with the local environment, the states allow for teleportation with genuinely quantum fidelity. The surprising fact here is that the necessary interaction does not require any intelligent action from the parties sharing the states. In passing, we produce some general results regarding optimization of teleportati…
We investigate the performance of quantum teleportation under a lossy environment using two different types of optical hybrid qubits. One is the hybrid of the vacuum and single-photon states with coherent states and the other is the hybrid of polarized single-photon states with coherent states. We have shown that the hybrid qubit using vacuum and single-photon states is generally more robust to photon loss effects compared to the one using the photon polarization with respect to fidelities and success probabilities of quantum teleportation.
Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry. However, their performance has been examined to date only within an idealistic noise model. Here, we further analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. To this end, we numerically compute the average gate fidelity, including measu…
A class of quantum protocols to teleport bipartite (entangled) states of two qubits is suggested. Our schemes require a single entangled pair shared by the two parties and the transmission of three bits of classical information, as well as a two-qubit gate with an additional qubit at the receiver' location. Noisy quantum channels are considered and the effects on both the teleportation fidelity and the entanglement of the replica are evaluated.
Port-based teleportation under pure-dephasing decoherence
Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）；International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子技术理论国际中心）
We study standard quantum teleportation of one-qubit state for the situation in which the channel is subject to decoherence, and where the evolution of the channel state is ruled by a master equation in the Lindblad form. A detailed calculation reveals that the quality of teleportation is determined by both the entanglement and the purity of the channel state, and only the optimal matching of them ensures the highest fidelity of standard quantum teleportation. Also our results demonstrated that the decoherence induces distortion of the Bloch sphere for the output state with different rates in …
