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arXiv:1303.3637 · Journal of Physics A Mathematical and Theoretical

An investigation of the transfer dynamics of quantum teleportation by weak measurement statistics

Masanori Hiroishi, Holger Friedrich Hofmann

Published May 30, 2013• 5 citations
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Abstract

We explore the mechanism of quantum teleportation by analyzing the weak measurement statistics post-selected by the result of the Bell measurement for the joint system composed of the input A and the spatially separated output B . It is shown that the weak measurement statistics observed before the Bell measurement includes correlations which relate every physical property in the input A to a corresponding physical property in the output B . The Bell measurement thus identifies the accidental relation between A and B already present in the quantum fluctuations of the input state. Significantly, this relation applies to all physical properties equally, and is completely independent of the input state. Teleportation therefore copies all physical properties of input system A to output system B , irrespective of whether the input state is an eigenstate of the property or not.

DOI
10.1088/1751-8113/46/24/245302

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We explore the mechanism of quantum teleportation by analyzing the weak measurement statistics post-selected by the result of the Bell measurement for the joint system composed of the input A and the spatially separated output B . It is shown that the weak measurement statistics observed before the Bell measurement includes correlations which relate every physical property in the input A to a corresponding physical property in the output B . The Bell measurement thus identifies the accidental relation between A and B already present in the quantum fluctuations of the input state. Significantly, this relation applies to all physical properties equally, and is completely independent of the input state. Teleportation therefore copies all physical properties of input system A to output system B , irrespective of whether the input state is an eigenstate of the property or not.
Quantum teleportation is a method to transfer unknown quantum states to a distant place with an assist of quantum entanglement. Whole process of the teleportation can be described by a transfer-operator. It allows us to calculate the output state in the case of the teleportation using non-maximal entanglement. This method investigates the properties of some of the output states. The photon statistics of the teleportation output are determined and the correlation between the field information β obtained in the teleportation process and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of a qubit encoded in the polarization of a single-photon state.
Quantum teleportation is possible because entanglement allows a definition of precise correlations between the noncommuting properties of a local system and corresponding noncommuting properties of a remote system. In this paper, the exact causality achieved by maximal entanglement is analyzed and the results are applied to the transfer of effects acting on the entanglement distribution channels to the teleported output state. In particular, it is shown how measurements performed on the entangled system distributed to the sender provide information on the teleported state while transferring the corresponding backaction to the teleported quantum state.
Teleporting a quantum state,the sender Alice disassembles the entire informations into two parts: one purely classical information and the another purely non-classical information,then sends them to the receiver Bob via two different channels.Firstly,sending the purely non-classical part,the EPR pair which consists of two fermions with the spin of 1 2 here plays the key role in the teleportation,one EPR particle is given to Alice,while the other is given to Bob.Alice performs a complete measurement of the von Neumann type on the joint system consisting of the original particle and her EPR particle,this measurement performed in the four eigenstates of the Bell operator leads to collapse the wave packet of the joint wavefunction into the four correlated Bell bases.Through applying the appropriate unitary transformation to the state of his EPR particle Bob can reconstruct a replica of the original state destroyed in Alice's hand.Moreover,this Bell measurement produces two bits of classical information which is sent to Bob,a quantum teleportation is therefore completed.The paper studies the interior relation between EPR pairs of particles and the quantum teleportation.
A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but nonpositive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems, resulting in perfect correlations for all observables. The joint probabilities for noncommuting measurements on separate clones then correspond to the real parts of the complex joint probabilities observed in weak measurements on a single system, where the measurements on the two clones replace the corresponding sequence of weak measurement and postselection. The imaginary parts of weak measurement statics can be obtained by replacing the cloning process with a partial swap operation. A controlled-swap operation combines both processes, making the complete weak measurement statistics accessible as a well-defined contribution to the joint probabilities of fully resolved projective measurements on the two output systems.
Quantum teleportation is a very helpful information-theoretic protocol that allows to transfer an unknown arbitrary quantum state from one location to another without having to transmit the quantum system through the intermediate region. Quantum states, quantum channels, and indefinite causal structures are all examples of quantum causal structures that not only enable advanced quantum information processing functions, but can also model causal structures in nonclassical spacetimes. In this letter, we develop quantum teleportation of arbitrary quantum causal structures, as formalized by the process matrix framework. Instead of teleporting all the physical degrees of freedom that implement the causal structure, the central idea is to just teleport the inputs to and outputs from the operations of agents. The communication of outcomes of Bell state measurements, which is necessary for deterministic quantum teleportation, is not possible for all causal structures that one might wish to investigate. To avoid this problem, we propose partially and fully post-selected teleportation protocols. We prove that our partially post-selected teleportation protocol is compatible with all quantum causal structures, including those that involve indefinite causal order.
It is widely assumed that the quantum fluctuations of the meter readout in a weak measurement make it impossible to identify the contributions originating from the individual values of the physical property observed in the measurement. Here, we show that a careful analysis of the quantum dynamics of the meter system allows us to identify a universal relation between quantum interference in the post-selection probability, and quantum interference in the statistics of the meter readout. The analysis reveals that quantum interference modifies the readout distribution of the meter in two ways, a diffusion term that identifies the appropriate operator ordering in the post-selected variance of the observed system property, and a wavefunction-dependent update of the initial meter statistics based on the effect of back action on the post-selection probability. Our results show that the statistical patterns described by meter interference provide important details about the physics of post-selection in weak measurements, allowing us to exclude the possibility of statistical artefacts in the experimental observation of weak values.