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Frontiers in Optics

Reduced Decoherence of Macroscopic States Using Squeezing and Anti-Squeezing

R. A. Brewster, J. D. Franson

Published Jan 1, 2018• 0 citations
Publisher

Abstract

The decoherence of macroscopic quantum states due to loss can be reduced by squeezing before transmission, followed by amplification and anti-squeezing to restore the original amplitude. This approach does not decrease the data transmission rate.
DOI
10.1364/fio.2018.jw4a.66

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Loss and decoherence are major problems in the transmission of nonclassical states of light over large distances. It was recently shown that the effects of decoherence can be reduced by applying a probabilistic noiseless attenuator before transmitting a quantum state through a lossy channel, followed by probabilistic noiseless amplification [M. Micuda, I. Straka, M. Mikova, M. Dusek, N. J. Cerf, J. Fiurasek, and M. Jezek, Phys. Rev. Lett. 109, 180503 (2012)]. Here we show that similar results can be obtained for certain kinds of macroscopic quantum states by squeezing the signal before transmission, followed by deterministic amplification and antisqueezing to restore the original amplitude of the state. This approach can greatly reduce the effects of decoherence in the transmission of non-Gaussian states, such as Schr\"odinger cat states, without any reduction in the data transmission rate.
Quantum information is a field with many potential applications in future technology. One of the major challenges in the practical implementation of quantum information protocols is the difficulty in synthesizing and maintaining controllable quantum systems. One of the reasons for this is because quantum systems are susceptible to decoherence that reduces the quality of the quantum state of a system. There have been several advances toward mitigating this decoherence such as the design of codes to combat errors due to incoherent quantum evolution, known as quantum error correction, and the design of novel quantum states that are less susceptible to decoherence. In this dissertation, we provide a rigorous analysis of the mechanisms that introduce decoherence into select quantum states and propose methods to compensate for it. We find that squeezing a macroscopic quantum optical state known as a Schrödinger cat state can reduce the amount of decoherence introduced by optical parametric amplification. We also find that noiseless amplification can be used to compensate for decoherence due to polarization dependent loss in single-photonic polarization qubits. In the process of understanding decoherence and its compensation we also introduce new and exciting mathematical and physical concepts such as delta functions that admit complex arguments, known as the generalized delta function, and a noiseless attenuator made using an optical parametric amplifier.
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We present a protocol which allows for arbitrary optical quantum states to simultaneously carry and transmit classical data, without sacrificing the integrity of either the quantum or classical information. Our scheme encodes classical information via displacements in the phase space prior to transmission and retrieves each classical symbol via a Gaussian continuous-variable teleportation. The original quantum state is then restored by guessing the the original displacement and performing the appropriate inverse operation. In the limit of sufficiently high classical signal and high squeezing, we show that our scheme is capable of perfectly reconstructing both the input classical signal and the input quantum state without loss of coherence. An example is given in terms of the transmission of a dual-rail Bell state.
Recent work by Mi\ifmmode \check{c}\else \v{c}\fi{}uda et al. [Phys. Rev. Lett. 109, 180503 (2012)] suggests that pairing noiseless amplification with noiseless attenuation can conditionally suppress loss terms in the direct transmission of quantum states. Here we extend this work to entangled states: First, we explore bipartite states, specifically the two-mode squeezed vacuum and NOON states, and, second, we examine MMM-partite states, concentrating on W and Greenberger-Horne-Zeilinger (GHZ) states. In analogy with the original proposal, our results demonstrate that in each case under consideration, a correct combination of attenuation and amplification techniques before and after transmission through a pure loss channel can restore the initial quantum state. However, we find that for both W and NOON states, the noiseless attenuation is redundant and not required to achieve loss term suppression. This work clarifies the role of noiseless attenuation when paired with noiseless amplification for entanglement distribution and provides an operational example of how GHZ and W state entanglement differs.