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arXiv:quant-ph/0008038 · Physical Review A

Transfer of quantum states using finite resources

Dietmar G. Fischer, Holger Mack, Matthias Freyberger

Published Mar 16, 2001• 13 citations
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Abstract

We discuss the problem of transfering a qubit from Alice to Bob using a noisy quantum channel and only finite resources. As the basic protocol for the transfer we apply quantum teleportation. It turns out that, for a certain quality of the channel, direct teleportation combined with qubit purification is superior to entanglement purification of the channel. If, however, the quality of the channel is rather low, one should simply apply an estimation-preparation scheme.

DOI
10.1103/physreva.63.042305

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We discuss the problem of transfering a qubit from Alice to Bob using a noisy quantum channel and only finite resources. As the basic protocol for the transfer we apply quantum teleportation. It turns out that, for a certain quality of the channel, direct teleportation combined with qubit purification is superior to entanglement purification of the channel. If, however, the quality of the channel is rather low, one should simply apply an estimation-preparation scheme.
In this work, we study quantum teleportation, a fundamental protocol of quantum physics. In particular, we present a mathematical methodology to study the combined effects of noisy resource state and noisy classical communication on teleportation fidelity and its deviation. We describe a teleportation protocol where an arbitrary two-qubit state in canonical form is used as a resource. Thereafter, to teleport an unknown qubit, Alice measures her qubits in Bell basis and conveys the measurement outcome to Bob via noisy classical channel(s). We derive the exact formulae of optimal teleportation fidelity and corresponding fidelity deviation where the resource state and the classical communication, both can be noisy. To provide the proof of optimality, we provide a systematic method. We further find conditions for non-classical fidelity and dispersion-free teleportation for our teleportation protocol. In this way, we identify noisy environments where it is possible to achieve dispersion-free teleportation without compromising non-classical fidelity. We also demonstrate scenarios where the increase of entanglement in the resource state, may degrade the quality of teleportation — a counter-intuitive instance. Finally, we discuss about the minimum classical communication cost required to achieve non-classical fidelity for our protocol. Here we mainly focus on a possible way to optimize the classical communication cost.
The quantum teleportation with a 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 , where 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 to the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompositions for the 3-qubit mixed states are discussed by adopting a teleportation with a W-state.
Quantum teleportation uses a shared entangled resource, local operations, and a digitally error-corrected classical channel to transfer quantum states between distant parties. We introduce a hybrid teleportation-direct transmission protocol for state transfer that still exploits entanglement, but replaces classical communication and digital error correction with an analog feedforward through a noisy quantum channel. We show that quantum teleportation outperforms this protocol if the communication channel reduces the entanglement of all bipartite states having the same amount of entanglement as the resource; otherwise, the hybrid protocol is optimal. We apply our result to the state transfer of a uniformly distributed coherent-states codebook, highlighting experimentally relevant scenarios where our protocol is most effective. Our findings are directly relevant to both optical and superconducting microwave channels, where analog feedforward techniques have been recently implemented.
Quantum teleportation uses a shared entangled resource, local operations, and a digitally error-corrected classical channel to transfer quantum states between distant parties. We introduce a hybrid teleportation-direct transmission protocol for state transfer that still exploits entanglement, but replaces classical communication and digital error correction with an feedforward through a noisy quantum channel. We show that quantum teleportation outperforms this protocol if the communication channel reduces the entanglement of all bipartite states having the same amount of entanglement as the resource; otherwise, the hybrid protocol is optimal. We apply our result to the state transfer of a uniformly distributed coherent-states codebook, highlighting experimentally relevant scenarios where our protocol is most effective. Our findings are directly relevant to both optical and superconducting microwave channels, where analog feedforward techniques have been recently implemented.
Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed by the sender (Alice), and classical information sent to the receiver (Bob) are three key ingredients in the procedure, which need to cooperate with each other. To study the relationship among the three parts, we propose a scheme for perfect teleportation of a qubit through a high-dimensional quantum channel in a pure state with two equal largest Schmidt coefficients. The scheme requires less entanglement of Alice's measurement but more classical bits than the original scheme via a Bell state. The two quantities increase with the entanglement of the quantum channel when its dimension is fixed and thereby can be regard as Alice's necessary capabilities to use the quantum channel. And the two capabilities appear complementary to each other.
Recently, there is much interest in the study of quantum teleportation. Its marvelous security property makes it particularly attractive as potential means for future communication. Uncertain principal and no-cloning theories of quantum mechanics forbid exact copy of quantum states. To solve the problem, quantum teleportation devides message state into two parts: classical message and quantum message which are transmitted through relevant classical and quantum channels from a sender Alice to a distant receiver Bob, respectively. According to both message states, Bob can recover the original message state with certain possibility. Utilizing the general quantum teleportation protocol, in this scheme, a new method is presented by which multi-qubit quantum information can be teleported in a much easier way. It has been extended to teleportation of an arbitrary N-qubit state via entanglement swapping and probabilistic teleportation is investigated as well, which has a more general meaning. N non-maximally entangled triplet GHZ states (Greenberger-Home-Zeilinger), taking the place of the previous EPR states (Einstein-Podolsky-Rosen), serve as quantum channels, which avoids introducing extra auxiliary qubit. In order to complete the teleportation, Alice has to devide all qubits into N parts and make Bell-State measurement on qubit pair (i, x(subscript i)) and tell Bob the measurement result through classical channel, then Bob perform some simple local operations on qubits (y(subscript i), z(subscript i)) to finish teleporting the i-th qubit. Conditioned on N-times similar repeat, Bob can faithfully reconstruct the initial state. Results show that, in this method, the identification difficulty of entangled states is considerably reduced, the new method is more feasible in technique. And the total possibility of successful teleportation is (The equation is abbreviated). As a special case, teleportation of an arbitrary two-qubit state is proposed.