We investigate chain teleportation of a qutrit-state via the non-maximally two-qutrit entangled channels. For the case of four parties, the efficiencies of two chain teleportation protocols, the separate chain teleportation protocol (SCTP) and the global chain teleportation protocol (GCTP), are calculated. In SCTP the errors are corrected between every step while in GCTP the errors are corrected only at the end. Furthermore, we present a piecewise global chain teleportation protocol (PGCTP) for keeping away from the inconvenience of error-correction of GCTP. We show that PGCTP is more efficient than SCTP.
Quantum entanglement, like othre resources, is now coonsidered to be a resource which can be produced, concentrated if required, transported and consumed. After its inception [1] in 1933, various schemes of quantum state teleportation have been proposed using different types of channels. Not restricting to qubit based systems, qutrit states and channels have also been of considerable interest. In the present paper we investigate the teleportation of an unknown single qutrit state as well as two qutrit state through a three qutrit quantum channel along with the required operations to recover th…
Since the initial discovery of quantum teleportation, it is devoted to transferring unknown quantum states from one party to another distant partner. However, in the scenarios of remote sensing, what people truly care about is the information carried by certain parameters. The problem of multiparameter estimation in the framework of qutrit teleportation under amplitude damping (AD) noise is studied. Particularly, two schemes are proposed to battle against AD noise and enhance the precision of multiparameter estimation by utilizing weak measurement (WM) and environment-assisted measurement (EAM…
Teleportation witnesses are hermitian operators which can identify useful entanglement for quantum teleportation. Here we provide a systematic method to construct teleportation witnesses from entanglement witnesses corresponding to general qudit systems. The witnesses so constructed are shown to be optimal for qubit and qutrit systems, and therefore detect the largest set of states useful for teleportation within a given class. We demonstrate the action of the witness pertaining to different classes of states in qubits and qutrits. Decomposition of the witness in terms of spin operators facili…
Two-body control of noiseless subsystems with mixed $SU(3)$ representations lifts teleportation above the classical fidelity limit
International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk（格但斯克大学量子技术理论国际中心）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）
The theory of quantum information provides a common language which links disciplines ranging from cosmology to condensed-matter physics. For example, the delocalization of quantum information in strongly-interacting many-body systems, known as quantum information scrambling, has recently begun to unite our understanding of black hole dynamics, transport in exotic non-Fermi liquids, and many-body analogs of quantum chaos. To date, verified experimental implementations of scrambling have dealt only with systems comprised of two-level qubits. Higher-dimensional quantum systems, however, may exhib…
Bell state measurements, in which two quantum bits are projected onto a maximally entangled state, are an essential component of quantum information science. We propose and experimentally demonstrate the projection of two quantum systems with three states (qutrits) onto a generalized maximally entangled state. Each qutrit is represented by the polarization of a pair of indistinguishable photons - a biphoton. The projection is a joint measurement on both biphotons using standard linear optics elements. This demonstration enables the realization of quantum information protocols with qutrits, suc…
We describe two protocols for efficient data transmission using a single passive bus. Different types of interactions are obtained enabling deterministic transfer and teleportation of composite quantum systems for arbitrary subsystem dimension and for arbitrary numbers of subsystems. The subsystems may become entangled in the transmission in which case the protocols can serve generalized teleportation based information processing as well as storage and transmission functions. We explore the cases of two qubits and two qutrits in detail, obtaining a maximally entangling mapping of the composite…
We propose a scheme for probabilistic teleportation of an unknown two-particle state of general formation in ion trap. It is shown that one can realize experimentally this teleportation protocol of two-particle state with presently available techniques.
We proposed a general transformation in probabilistic teleportation, which is based on different entanglement matching coefficients $K$ corresponding to different unitary evolution which provides one with more flexible evolution method experimentally. Through analysis based on the Bell basis and generalized Bell basis measurement for two probabilistic teleportation, we suggested a general probability of successful teleportation, which is not only determined by the entanglement degree of transmission channels and measurement methods, but also related to the unitary transformation in the telepor…
In this letter, two different probabilistic teleportations of a two-particle entangled state by pure entangled three-particle state are shown. Their successful probabilities are different.
We propose a scheme for probabilistic teleportation of unknown two-particle state with partly entangled four-particle state via POVM. In this scheme the teleportation of unknown two-particle state can be realized with certain probability by performing two Bell state measurements, a proper POVM and a unitary transformation.
We present a scheme for probabilistic teleportation via a non-maximally entangled GHZ state. Quantum teleportation will succeed with a certain probability if the sender makes a generalized Bell state measurement, the cooperator performs a generalized $X$ basis measurement, and the receiver introduces an auxiliary particle, performs a collective unitary transformation and makes a measurement on the auxiliary particle. The success probability of the teleportation is given. We also obtain the maximum of the success probability of the teleportation.
A simplification scheme of probabilistic teleportation of two-particle state of general form is given. By means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations, we construct an efficient quantum logical network for implementing the new scheme of probabilistic teleportation of a two-particle state of general form.
The scheme for probabilistic teleportation of an N-particle state of general form is proposed. As the special cases we construct efficient quantum logic networks for implementing probabilistic teleportation of a two-particle state, a three-particle state and a four-particle state of general form, built from single qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations.
We propose a scheme for building a heralded two-qutrit entangled state from polarized photons. An optical circuit is presented to build the maximally entangled two-qutrit state from two heralded Bell pairs and ideal threshold detectors. Several schemes are discussed for constructing the two Bell pairs. We also show how one can produce an unbalanced two-qutrit state that could be of general purpose use in some protocols. In terms of applications of the maximally entangled qutrit state, we mainly focus on how to use the state to demonstrate a violation of the Collins-Gisin-Linden-Massar-Popescu …
We propose a novel scheme for probabilistic teleportation when the information of the partially entangled state is only available for the sender. This is in contrast with the fact that the receiver must know the non-maximally entangled state in previous typical schemes for the teleportation. Additionally, we illustrate two potential applications of the novel scheme to probabilistically teleport an unknown two-level quantum state from a sender to a receiver with the help of an assistant, who plays distinguishable roles under different communication conditions, and the applications indicate that…
In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, {\em do} support a teleportation protocol. We isolate a natural class of composite systems that we term {\em regular}, and establish necessary and sufficient conditions for a regular tripartite system to supp…
Teleportation is a quantum information processes without classical counterparts, in which the sender can disembodied transfer unknown quantum states to the receiver. In probabilistic teleportation through a partial entangled quantum channel, the transmission is exact (with fidelity 1), but may fail in a probability and the initial state is destroyed simultaneously. We propose a scheme for nondestructive probabilistic teleportation of high-dimensional quantum states. With the aid of an ancilla in the hands of the sender, the initial quantum information can be recovered when teleportation fails.…
We present simplification schemes for probabilistic and controlled teleportation of the unknown quantum states of both one-particle and two-particle and construct efficient quantum logic networks for implementing the new schemes by means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations. In these schemes the teleportation are not always successful but with certain probability.
Classical and Quantum Resources in Perfect Teleportation
Theoretical Physics Division, Chern Institute of Mathematics, Nankai University（南开大学陈省身数学研究所理论物理部）；Department of Physics, School of Science, Tianjin University（天津大学理学院物理系）
We consider a generalized quantum teleportation protocol for an unknown qubit using non-maximally entangled state as a shared resource. Without recourse to local filtering or entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity albeit with reduced probability, hence probabilistic teleportation. We also give a generalized protocol for entanglement swapping using non-maximally e…
Precise measurement or perfect cloning of unknown quantum states is forbidden by the laws of quantum mechanics. Yet, quantum teleportation in principle allows for a faithful and disembodied transmission of unknown quantum states between distant quantum systems using entanglement. There have been numerous experiments on teleportation of quantum states of single photons, atoms, trapped ions, defects in solid states, and superconducting circuits. However, all demonstrations to date were limited to a two-dimensional subspace$-$so-called qubit$-$of the quantized multiple levels of the quantum syste…
We study the entanglement of entangled coherent states in vacuum environment by employing the entanglement of formation and propose a scheme to probabilistically teleport a coherent superposition state via entangled coherent states, in which the amount of classical information sent by Alice is restricted to one bit. The influence of decoherence due to photon absorpation is considered. It is shown that decoherence can improve the mean fidelity of probabilistic teleportation in some situations.
It is known that if the shared resource is a maximally entangled state then it is possible to teleport an unknown state with unit fidelity and unit probability. However, if the shared resource is a non-maximally entangled state then one has to follow a probabilistic scheme where one can teleport a qubit with unit fidelity and non-unit probability. In this work, we investigate the feasibility of using partially entangled states as a resource for quantum teleportation of a qudit. We also give an expression for the probability of successful teleportation of an unknown qudit.
Teleportation may be taken as sending and extracting quantum information through quantum channels. In this report, it is shown that to get the maximal probability of exact teleportation through partially entangled quantum channels, the sender (Alice) need only to operate a measurement which satisfy an ``entanglement matching'' to this channel. An optimal strategy is also provided for the receiver (Bob) to extract the quantum information by adopting general evolutions.
Teleporation with partially entangled quantum channel cannot achieve unit fidelity and unit probability. We show that the conditions for faithful teleportation of a pure state or a mixed state can be described by the same general relation $ρ_{q}ρ_{m} = pI$, where $ρ_{q}$ is the reduced density matrix of the quantum channel, $ρ_{m}$ is the reduced density matrix of the measurement basis, and $p$ is the probability of faithful teleportaion. We investigate the invariance of faithful teleportation conditions under unitary transformation. These results not only bring new insights to the probabilist…
The no-cloning theorem forbids the distribution of an unknown state to more than one receiver. However, if the sender knows the state, and the state is chosen from a restricted set of possibilities, a procedure known as remote state preparation can be used to broadcast a state. Here we examine a remote state preparation protocol that can be used to send the state of a qubit, confined to the equator of the Bloch sphere, to an arbitrary number of receivers. The entanglement cost is less than that of using teleportation to accomplish the same task. We present a number of variations on this task, …
A non-standard teleportation scheme is proposed, wherein probabilistic teleportation is achieved in conventionally non-teleporting channels. We make use of entanglement monogamy to incorporate an unknown state in a multipartite entangled channel, such that the receiver partially gets disentangled from the network. Subsequently, the sender performs local measurement based teleportation protocol in an appropriate measurement basis, which results with the receiver in the possession of an unknown state, connected by local unitary transformation with the state to be teleported. This procedure succe…
In this work, we propose a probabilistic teleportation protocol to teleport a single qubit via three-qubit W-states using two-qubit measurement basis. We show that for the proper choice of the state parameter of the resource state, it is possible to make success probability of the protocol very high. We deduce the condition for the successful execution of our teleportation protocol and this gives us new class of three-qubit W-states which act as a resource state. We have constructed operators that can be used to verify the condition of teleportation in experiment. This verification is necessar…
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.
Improving the probabilistic quantum teleportation efficiency of arbitrary superposed coherent state using multipartite even and odd j-spin coherent states as resource
All existing quantum oblivious transfer protocols are to realize the oblivious transfer of bit or bit-string. In this paper, p-Rabin quantum oblivious transfer of a qubit (abbr. p-Rabin qubit-OT) is achieved by using a probabilistic teleportation (abbr. PT) protocol. Here, this is the first time that the concept of qubit-OT is presented. As the PT protocol is able to transfer an (un)known pure state with a certain probability, this feature makes the PT protocol well fit for Rabin OT. Furthermore, the PT protocol can be used for OT of a bit by encoding classical bit with two pre-agreed orthogon…
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…
We clarify the connections between the erasure scheme of probabilistic CNOT gate implementation recently proposed by Pittman, Jacobs and Franson [Phys. Rev. A 64, 062311 (2001)] and quantum teleportation.
We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $σ_{x}$. Both these measurement outcomes are communicated to Bob classical…
A scheme for teleporting an unknown two-particle entangled state via W class states is proposed. In this scheme, the W class entangled states are considered as quantum channels. It is shown that by means of optimal discrimination between two nonorthogonal quantum states, probabilistic teleportation of the two-particle entangled state can be achieved.
We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore error-free any of the two encoded qubit states but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have f…
We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is effectively computable and outperforms the explicit values of the entanglement fidelity calculated for the pre-existing variants of the port-based protocols, allowing for teleportation of a much larger amount of quantum information. The comparison with the exact formulas and similar analysis for the probabilistic scheme is also discussed. In particular, we present the…
Quantum teleportation is a powerful protocol with applications in several schemes of quantum communication, quantum cryptography and quantum computing. The present work shows the required conditions for a two-qubit quantum gate to be deterministically and probabilistically teleported by a quantum gate teleportation scheme using different basis of measurement. Additionally, we present examples of teleportation of two-qubit gates that do not belong to Clifford group as well the limitations of the quantum gate teleportation scheme employing a four-qubit state with genuine four-way entanglement.
We extend the research program initiated in [Phys. Rev. A 92, 012338 (2015)], where we restricted our attention to noisy deterministic teleportation protocols, to noisy probabilistic (conditional) protocols. Our main goal now is to study how we can increase the fidelity of the teleported state in the presence of noise by working with probabilistic protocols. We work with several scenarios involving the most common types of noise in realistic implementations of quantum communication tasks and find many cases where adding more noise to the probabilistic protocol increases considerably the fideli…
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and two-qutrit unitary operations as well as post-selection according to the results obtained in intermediate measurements. We utilize the nonlinear transformation in an algorithm to identify a quantum state provided it belongs to an arbitrary known finite set. The algorithm is based on dividing the known set of states into two appropriately designed subsets which…
The scheme of quantum teleportation, where Bob has multiple (N) output ports and obtains the teleported state by simply selecting one of the N ports, is thoroughly studied. We consider both deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state, and (ii) the state is also optimized as well as Alice's measurement. We analytically determine the optimal protocols for all the four cases, and show …
