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arXiv:2002.12651 · Physical Review A

Generalization of port-based teleportation and controlled teleportation capability

Kabgyun Jeong, Jaewan Kim, Soojoon Lee

Published Jul 10, 2020• 17 citations
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Abstract

As a variant of the original quantum teleportation, port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a $2M$-qudit state, then it can be expressed as $M$ copies of a two-qudit maximally entangled state, where $M$ is the number of ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of controlled port-based teleportation by combining controlled teleportation with port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present quantities called the control power and the minimal control power for the controlled version on a given tripartite quantum state.

DOI
10.1103/physreva.102.012414

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As a variant of the original quantum teleportation, port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a 2M2M2M-qudit state, then it can be expressed as MMM copies of a two-qudit maximally entangled state, where MMM is the number of ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of controlled port-based teleportation by combining controlled teleportation with port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present quantities called the control power and the minimal control power for the controlled version on a given tripartite quantum state.
We consider the controlled quantum teleportation performed on a single copy of entangled three-qubit pure states and show how the fidelity of teleportation and the control power are related to the tripartite entanglement measures, namely, three-tangle and genuine concurrence. We characterize the states with extreme properties, and use them to derive tight lower and upper bounds on both the teleportation fidelity and control power for a given amount of entanglement. Furthermore, we discuss the usefulness of these two quantities for experimental detection and/or quantification of tripartite entanglement. In particular, we present the results which imply that the control power cannot be considered as a candidate for a degree of three-qubit entanglement complementary to the three-tangle as conjectured recently [K. Jeong, J. Kim, and S. Lee, Phys. Rev. A 93, 032328 (2016)]. Furthermore, we prove a mutual relation between teleportation fidelity and control power which provides attainable limits of the controller's authority for existing controlled teleportation schemes. Although those relations are derived for pure states, their extensions for mixed states are also examined.
In our work we propose a generalization of the port-based teleportation scheme, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob's side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where the resource state is maximally entangled. It turns out that the new scheme gives better performance than the optimal PBT protocol with the respective larger dimension of the port. We exploit the same number of maximally entangled states in the resource state as in the ordinary port-based teleportation with a number of measurements scaling polynomially in the number of shared maximally entangled states. To obtain our results, i.e. explicit expressions for the performance of the new scheme, we deliver novel mathematical tools concerning representation theory of the algebra of partially transposed permutation operators, where the transposition acts on more than one subsystem.
Abstract In standard quantum teleportation, the receiver must wait for a classical message from the sender before subsequently processing the transmitted quantum information. However, in port-based teleportation (PBT), this local processing can begin before the classical message is received, thereby allowing for asynchronous quantum information processing. Motivated by resource-theoretic considerations and practical applications, we propose different communication models that progressively allow for more powerful decoding strategies while still permitting asynchronous distributed quantum computation, a salient feature of standard PBT. Specifically, we consider PBT protocols augmented by free classical processing and/or different forms of quantum pre-processing, and we investigate the maximum achievable teleportation fidelities under such operations. Our analysis focuses specifically on the PBT power of isotropic states, bipartite graph states, and symmetrized EPR states, and we compute tight bounds on the optimal teleportation fidelities for such states. We finally show that, among this hierarchy of communication models consistent with asynchronous quantum information processing, the strongest resource theory is equally as powerful as any one-way teleportation protocol for surpassing the classical teleportation threshold. Thus, a bipartite state can break the one-way classical teleportation threshold if and only if it can be done using the trivial decoding map of discarding subsystems.
Teleportation for pure states, mixed states with standard and optimal protocols are introduced and investigated systematically. An explicit equation governing the teleportation of finite dimensional quantum pure states by a generally given non-local entangled state is presented. For the teleportation of a mixed state with an arbitrary mixed state resource, an explicit expression is obtained for the quantum channel associated with the standard teleportation protocol. The corresponding transmission fidelity is calculated. It is shown that the standard teleportation protocol is not optimal. The optimal quantum teleportation is further studied, its fidelity is given and shown to be related to the fully entangled fraction of the quantum resource, rather than the single fraction as in the standard teleportation protocol.
In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports N , the number of teleported systems k , and local dimension d . It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number N of ports increases as o(N) still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.
The scheme of quantum teleportation, where Bob has multiple (N)(N)(N) output ports and obtains the teleported state by simply selecting one of the NNN ports, is thoroughly studied. We consider both the 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 the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$. The entanglement properties of the teleportation scheme are also discussed.