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arXiv:quant-ph/0512069 · Physical Review A

Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states

Akira Kitagawa, Masahiro Takeoka, Masahide Sasaki, Anthony Chefles

Published Apr 10, 2006• 225 citations
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Abstract

We consider the problem of evaluating the entanglement of non-Gaussian mixed states generated by photon subtraction from entangled squeezed states. The entanglement measures we use are the negativity and the logarithmic negativity. These measures possess the unusual property of being computable with linear algebra packages even for high-dimensional quantum systems. We numerically evaluate these measures for the non-Gaussian mixed states which are generated by photon subtraction with on/off photon detectors. The results are compared with the behavior of certain operational measures, namely the teleportation fidelity and the mutual information in the dense coding scheme. It is found that all of these results are mutually consistent, in the sense that whenever the enhancement is seen in terms of the operational measures, the negativity and the logarithmic negativity are also enhanced.

DOI
10.1103/physreva.73.042310

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We consider the problem of evaluating the entanglement of non-Gaussian mixed states generated by photon subtraction from entangled squeezed states. The entanglement measures we use are the negativity and the logarithmic negativity. These measures possess the unusual property of being computable with linear algebra packages even for high-dimensional quantum systems. We numerically evaluate these measures for the non-Gaussian mixed states which are generated by photon subtraction with on/off photon detectors. The results are compared with the behavior of certain operational measures, namely the teleportation fidelity and the mutual information in the dense coding scheme. It is found that all of these results are mutually consistent, in the sense that whenever the enhancement is seen in terms of the operational measures, the negativity and the logarithmic negativity are also enhanced.
The photon subtraction operation is an effective method to enhance an entanglement of the two-mode squeezed vacuum state. We show that it can be well approximated to the two-mode squeezed state with an enhanced squeezing although it is basically a mixed and non-Gaussian state. Such property can be directly observed by the current technology. We also study the continuous variable quantum dense coding with the photon subtracted two-mode squeezed state. It is shown that, in particular squeezing region, its error probability performance can be greatly improved from the original two-mode squeezed state. Since quantum dense coding is the protocol to transmit classical information, our analysis provides an alternative operational meaning of the entanglement involved in the on-off photon subtracted state, compared to the previous results, such as teleportation or the nonlocality, that could help to quantify the entanglement of mixed and non-Gaussian states.
We investigate the entanglement swapping of non-Gaussian states, including squeezed number states, two-mode photon-added states, and two-mode photon-subtracted squeezed states and analyze the entanglement of the swapped states by adopting logarithmic negativity as the measure of entanglement. Furthermore, we examine the fidelity of teleportation protocols for different input states where the swapped states serve as the quantum channel. All these results are compared with that obtained in the case of Gaussian two-mode squeezed vacuum.
The entanglement properties of non-Gaussian states are investigated, which are obtained by performing the photon addition, photon subtraction, photon-addition-then-subtraction, and photon-subtraction-then-addition operations on the two-mode squeezed vacuum state. We show that the partial von Neumann entropy of all the resulting states is greater than that of the original squeezed state, but only the photon-subtracted states and the photon-added-then-subtracted states have the stronger Einstein-Podolsky-Rosen correlation than the original squeezed state. Quantum teleportation of Braunstein and Kimble protocol is studied for coherent states, squeezed states, and mixed Gaussian states with the non-Gaussian entangled resources. For all the states to be teleported, the fidelity with the photon-subtracted and the photon-added-then-subtracted entangled resources is higher than that with the two-mode squeezed vacuum resource. Based on Bures fidelity, we find that quantum teleportation for mixed and classical single-mode Gaussian states is more faithful than for single-mode Gaussian states with high purity and nonclassicality.
We show that the Fisher information associated with entanglement-assisted coding has a monotonic relationship with the logarithmic negativity, an important entanglement measure, for certain classes of continuous variable (CV) quantum states of practical significance. These are the two-mode squeezed states and the non-Gaussian states obtained from them by photon subtraction. This monotonic correspondence can be expressed analytically in the case of pure states. Numerical analysis shows that this relationship holds to a very good approximation even in the mixed state case of the photon-subtracted squeezed states. The Fisher information is evaluated by the CV Bell measurement in the limit of weak signal modulation. Our results suggest that the logarithmic negativity of certain sets of non-Gaussian mixed states can be experimentally accessed without homodyne tomography, leading to significant simplification of the experimental procedure.
We study the measurement-induced non-Gaussian operation on the single- and two-mode \\textit{Gaussian} squeezed vacuum states with beam splitters and on-off type photon detectors, with which \\textit{mixed non-Gaussian} states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states, we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.
We study the measurement-induced non-Gaussian operation on the single- and two-mode Gaussian squeezed vacuum states with beam splitters and on-off type photon detectors, with which mixed non-Gaussian states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states, we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.