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Register a new userProbabilistic resumable quantum teleportation in high dimensions
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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 simultaneously destroy the state to be teleported. We propose a scheme for nondestructive probabilistic teleportation of high-dimensional quantum states. With the aid of an ancilla in the hands of sender, the initial quantum information can be recovered when teleportation fails. The ancilla acts as a quantum apparatus to measure the senders subsystem, and erasing the information it records can resumes the initial state.
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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 systems. In general, a quantum particle can naturally possess not only multiple degrees of freedom, but also, many degrees of freedom can have high quantum number beyond the simplified two-level subspace. Here, making use of multiport beam-splitters and ancillary single photons, we propose a resource-efficient and extendable scheme for teleportation of arbitrarily high-dimensional photonic quantum states. We report the first experimental teleportation of a qutrit, which is equivalent to a spin-1 system. Measurements over a complete set of 12 states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), well above the optimal single-copy qutrit-state-estimation limit of 1/2. The fidelity also exceeds the limit of 2/3, the maximum possible for explanation through qubits only. Thus, we strictly prove a genuine three-dimensional, universal, and highly non-classical quantum teleportation. Combining previous methods of teleportation of two-particle composite states and multiple degrees of freedom, our work provides a complete toolbox for teleporting a quantum particle intact. We expect that our results will pave the way for quantum technology applications in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.
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 entangled states.
The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and nearly diagonal semi-Clifford gates are particularly important: they admit efficient gate teleportation protocols that implement these gates with fewer ancillary quantum resources such as magic states. Despite the practical importance of these sets of gates, many questions about their structure remain open; this is especially true in the higher-dimensional qudit setting. Our contribution is to leverage the discrete Stone-von Neumann theorem and the symplectic formalism of qudit stabiliser mechanics towards extending results of Zeng-Cheng-Chuang (2008) and Beigi-Shor (2010) to higher dimensions in a uniform manner. We further give a simple algorithm for recursively enumerating all gates of the Clifford hierarchy, a simple algorithm for recognising and diagonalising semi-Clifford gates, and a concise proof of the classification of the diagonal Clifford hierarchy gates due to Cui-Gottesman-Krishna (2016) for the single-qudit case. We generalise the efficient gate teleportation protocols of semi-Clifford gates to the qudit setting and prove that every third level gate of one qudit (of any prime dimension) and of two qutrits can be implemented efficiently. Numerical evidence gathered via the aforementioned algorithms support the conjecture that higher-level gates can be implemented efficiently.
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.
I propose to replace the dual classical and nonlocal channels used for teleporting unknown quantum states in the original protocol (OP) [Bennett, C. H., et al. Phys. Rev. Lett. 70 1895 (1993)] by either (i) one single quantum channel or (ii) two nonlocal channels in order to turn the OP into an all-quantum teleportation (AQT) protocol. Ideally, N runs of single channel AQT can be achieved with a single Einstein-Podolsky-Rosen (EPR) pair, in contrast with the OP, which consumes N EPR pairs. In the two nonlocal channels proposal, Alice uses the superdense coding technique to send Bob her result, which makes AQT more economical than OP.
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