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Investigation on Measurable Fidelity Between Gaussian Mixed States in Continuous Variable Domain

Hailong Zhang, Pla Information

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

From the original definition of fidelity in a pure state,we first give the well defined expansion fidelity between two Gaussian mixed states.It is related to the variances of output and input states in quantum information processing.It could be convenient to quantify the quantum teleportation(quantum clone) experiment since the variances of input(output) state are measurable.Furthermore,we also show that the fidelity of a pure input state is smaller than that of a mixed input state in the same quantum information processing.

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From the original definition of fidelity in a pure state,we first give the well defined expansion fidelity between two Gaussian mixed states.It is related to the variances of output and input states in quantum information processing.It could be convenient to quantify the quantum teleportation(quantum clone) experiment since the variances of input(output) state are measurable.Furthermore,we also show that the fidelity of a pure input state is smaller than that of a mixed input state in the same quantum information processing.
In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information processing. It is convenient to quantify the quantum teleportation (quantum clone) experiment since the variances of the input (output) state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing.
A noisy Gaussian channel is defined as a channel in which an input field mode is subjected to random Gaussian displacements in phase space. We introduce the quantum fidelity of a Gaussian channel for pure and mixed input states, and we derive a universal scaling law of the fidelity for pure initial states. We also find the maximum fidelity of a Gaussian channel over all input states. Quantum cloning and continuous-variable teleportation are presented as physical examples of Gaussian channels to which the fidelity results can be applied.
The efficiency of continuous-variable quantum teleportation is typically quantified by fidelity especially in experiment. From the original definition of fidelity in two pure states, we give an expansion of fidelity which is related to the variances of output and input states. With a coherent or a squeezed input state, it is convenient to quantify the quantum teleportation experiment, since the variances of quadrature components of the input and output states are measurable. Furthermore, the fidelity was discussed when the quantum channel lies in the phase- and amplitude-noisy environment, which is unavoidable in experiment, and this showed that the effect of phase noise on teleportation is more sensitive than that of the amplitude-noisy environment. The classical fidelity limit of squeezed state quantum teleportation is also obtained when the entanglement resources do not exist.
Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in continuous-variable (CV) teleportation, i.e., the fidelity deviation as the figure of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non-Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different input scenarios: One is when input states are sampled from constrained uniform distribution while the other one is Gaussian suppression of the input states which again leads to a different classification of CV states according to their performance. The entire analysis is carried out in noiseless and noisy scenarios with noise being incorporated in the measurement and the shared channels. We also report that one type of noise can make the protocol robust against the other one, which leads to a ``constructive effect,'' and identify the noise models which are responsible for decreasing average fidelity and the increment in fidelity deviation.
Abstract No-cloning theorem, a profound fundamental principle of quantum mechanics, also provides a crucial practical basis for secure quantum communication. The security of communication can be ultimately guaranteed if the output fidelity via the communication channel is above the no-cloning bound (NCB). In quantum communications using continuous-variable (CV) systems, Gaussian states, more specifically, coherent states have been widely studied as inputs, but less is known for non-Gaussian states. We aim at exploring quantum communication covering CV states comprehensively with distinct sets of unknown states properly defined. Our main results here are (i) to establish the NCB for a broad class of quantum non-Gaussian states, including Fock states, their superpositions, and Schrodinger-cat states and (ii) to examine the relation between NCB and quantum non-Gaussianity (QNG). We find that NCB typically decreases with QNG. Remarkably, this does not mean that QNG states are less demanding for secure communication. By extending our study to mixed-state inputs, we demonstrate that QNG specifically in terms of Wigner negativity requires more resources to achieve output fidelity above NCB in CV teleportation. The more non-Gaussian, the harder to achieve secure communication, which can have crucial implications for CV quantum communications.