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Physical Review A

Entanglement generation by communication using squeezed states

Fumiaki Matsuoka, Akihisa Tomita, Atsushi Okamoto

Published Aug 12, 2013• 5 citations
Publisher

Abstract

In order to improve the error probability of generating entanglement by communication for quantum computation, we propose the use of squeezed light. When generating entanglement between two atoms by communication, the error probability can be reduced by increasing the distance between quantum states of probe light in phase space. The phase rotation of light depends on the atom-photon coupling strength and the light amplitude, which are limited in practice. A large error probability has been expected for coherent probe light. If we assume typical values of light amplitude and phase rotation, $\ensuremath{\alpha}=100$ and $\ensuremath{\theta}=0.01$, the error probability is estimated to be ${P}_{\mathrm{coh}}^{(\mathrm{min})}=0.14$ and ${P}_{\mathrm{coh}}^{(\mathrm{hom})}=0.23$ for minimum error discrimination and homodyne measurements. The error probability can be reduced to ${P}_{\mathrm{squ}}^{(\mathrm{min})}=1.73\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ and ${P}_{\mathrm{squ}}^{(\mathrm{hom})}=4.09\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ using squeezed coherent light, where the same values of the mean photon number and the phase rotation angle are assumed for the coherent light probe. These values satisfy the requirements for scalable quantum computation.

DOI
10.1103/physreva.88.022313

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•Jan 1, 2010•0 citations
In order to improve the error probability of generating entanglement by communication for quantum computation, we propose the use of squeezed light. When generating entanglement between two atoms by communication, the error probability can be reduced by increasing the distance between quantum states of probe light in phase space. The phase rotation of light depends on the atom-photon coupling strength and the light amplitude, which are limited in practice. A large error probability has been expected for coherent probe light. If we assume typical values of light amplitude and phase rotation, \ensuremathα=100\ensuremath{\alpha}=100\ensuremathα=100 and \ensuremathθ=0.01\ensuremath{\theta}=0.01\ensuremathθ=0.01, the error probability is estimated to be Pcoh(min)=0.14{P}_{\mathrm{coh}}^{(\mathrm{min})}=0.14Pcoh(min)​=0.14 and Pcoh(hom)=0.23{P}_{\mathrm{coh}}^{(\mathrm{hom})}=0.23Pcoh(hom)​=0.23 for minimum error discrimination and homodyne measurements. The error probability can be reduced to Psqu(min)=1.73\ifmmode×\else\texttimes\fi10\ensuremath−8{P}_{\mathrm{squ}}^{(\mathrm{min})}=1.73\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}Psqu(min)​=1.73\ifmmode×\else\texttimes\fi10\ensuremath−8 and Psqu(hom)=4.09\ifmmode×\else\texttimes\fi10\ensuremath−5{P}_{\mathrm{squ}}^{(\mathrm{hom})}=4.09\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}Psqu(hom)​=4.09\ifmmode×\else\texttimes\fi10\ensuremath−5 using squeezed coherent light, where the same values of the mean photon number and the phase rotation angle are assumed for the coherent light probe. These values satisfy the requirements for scalable quantum computation.
To implement fault-tolerant quantum computation, entanglement generation with low error probability and high success probability is required. In a previous paper, we proposed the use of squeezed coherent light as a probe to generate entanglement between two atoms by communication and showed that the error probability is reduced well below the threshold of fault-tolerant quantum computation [F. Matsuoka et al., Phys. Rev. A 88, 022313 (2013)]. In this paper, we investigate the effect of photon loss mainly due to finite coupling efficiency to the cavity. The error probability with photon loss is calculated using a beam-splitter model for homodyne measurement of probe light. We examine the optimum conditions of the amplitude of the probe light and the degree of squeezing to minimize the error probability. We show that the phase-squeezed probe light yields lower error probability than a coherent-light probe, even with photon losses. A fault-tolerant quantum computation algorithm can be implemented under 87% transmittance by concatenating a seven-qubit error correction code for the phase-flip error.
We study the use of squeezed light for qubit coherent control and compare it with the coherent-state control field case. We calculate the entanglement between a short pulse of resonant squeezed light and a two-level atom in free space and the resulting operation error. We find that the squeezing phase, the phase of the light field, and the atomic superposition phase all determine whether atom-pulse mode entanglement and the gate error are enhanced or suppressed. When averaged over all possible qubit initial states, the gate error would not decrease by a practically useful amount and would in fact increase in most cases. However, the enhanced entanglement may be of use in quantum communication schemes. We discuss the possibility of measuring the increased gate error as a signature of the enhancement of entanglement by squeezing.
The possibility is explicitly shown that the average probability of error is reduced and the transmission rate of information is enhanced by means of entangled input states to a communication channel. When two senders transmit some information to a receiver, they encode the information in the quadrature amplitudes of both modes of a two-mode squeezed vacuum state. The receiver performs a simultaneous measurement of the two quadrature amplitudes of the received two-mode state. In this case, if the average value of the photon number supplied to the communication system is not so small, the average probability of error becomes smaller than that of the communication system without entanglement. Furthermore, the transmission rate of information becomes larger than the quantum capacity of classical information of the communication system without entanglement.
Coherent lightwave communications systems are approaching a limit where the error rates and channel capacities are limited by the quantum properties of light. This is often referred to as the shot-noise limit. If ideal laser light is used in the system, there is no way to avoid this limit. However, new states of the light field called squeezed states have recently been developed that allow an improvement in error rates below the shot-noise limit. Squeezed light concepts and recent experiments are reviewed with emphasis on aspects important to coherent communications. It is shown that channel capacity can be improved using squeezed light by only a factor of two. Larger improvements are in principle possible for error rates, e.g. a factor of three reduction in the number of required photons per bit for a 10/sup -9/ bit error rate. An example of a recent high-performance system is described where optical losses and electronic noise reduce the improvement expected using squeezed light to the 10-20% level. It is concluded that squeezed light only offers significant improvement in bit error rates for very-high-efficiency systems.>
Two-mode squeezed light is an effective resource for quantum entanglement and shows a non-classical correlation between each optical mode. We are developing a two-mode squeezed light source to explore the possibility of quantum radar based on the quantum illumination theory. It is expected that the error probability for discrimination of target presence or absence is improved even in a lossy and noisy environment. We are also expecting to apply two-mode squeezed light source to quantum imaging. In this work we generated two-mode squeezed light and verify its quantum entanglement property towards quantum radar and imaging. Firstly we generated two independent single-mode squeezed light beams utilizing two sub-threshold optical parametric oscillators which include periodically-polled potassium titanyl phosphate crystals for the second order nonlinear interaction. Two single-mode squeezed light beams are combined using a half mirror with the relative optical phase of 90◦ between each optical field. Then entangled two-mode squeezed light beams can be generated. We observes correlation variances between quadrature phase amplitudes in entangled two-mode fields by balanced homodyne measurement. Finally we verified quantum entanglement property of two-mode squeezed light source based on Duan’s and Simon’s inseparability criterion.
In this thesis, we investigate the uses of entanglement and its verification in quantum communication. Typically, it is the presence of entanglement which allows quantum communication protocols to outperform their classical counterparts, or to achieve tasks which are infeasible with classical physics. Therefore, the verification of entanglement can provide fundamental tests to certify that experimental implementations of such protocols operate quantum mechanically. The main object here is to develop a verification procedure which is adaptable to a wide range of applications, and whose implementation has low requirements on experimental resources. We present such a procedure in the form of the Expectation Value Matrix. The structure of this thesis is as follows: Chapters 1 and 2 give a short introduction and background information on quantum theory and the quantum states of light. In particular, we discuss the basic postulates of quantum mechanics, quantum state discrimination, the description of quantum light and the homodyne detector. Chapter 3 gives a brief introduction to quantum information and in particular to entanglement, and we discuss the basics of quantum key distribution and teleportation. The general framework of the Expectation Value Matrix is introduced. The main matter of this thesis is contained in the subsequent three chapters, which describe different quantum communication protocols and the corresponding adaptation of the entanglement verification method. The subject of Chapter 4 is quantum key distribution, where the detection of entanglement is a means of excluding intercept-resend attacks, and the presence of quantum correlations in the raw data is a necessary precondition for the generation of secret key. We investigate a continuous-variable version of the two-state protocol and develop the Expectation Value Matrix method for such qubit-mode systems. Furthermore, we analyse the role of the phase reference with respect to the security of the protocol and raise awareness of a corresponding security threat. For this, we adapt the verification method to different settings of Stokes operator measurements. In Chapter 5, we investigate quantum memory channels and propose a fundamental bench- mark for these based on the verification of entanglement. After describing some physical effects which can be used for the coherent storage of light, we focus on the storage of squeezed light. This situation requires an extension of our verification procedure to sources of mixed input states. We propose such an extension, and give a detailed analysis of its application to squeezed thermal states, displaced thermal states and mixed qubit states. This is supplemented by finding the optimal entanglement-breaking channels for each of these situations, which provides us with an indication of the strength of the extension to our entanglement criterion. The subject of Chapter 6 is also the benchmarking of quantum memory or teleportation experiments. Considering a number of recently published benchmark criteria, we investigate the question which one is most useful to actual experiments. For this, a criterion must be both strong, i.e., easy to overcome, and it must be implementable with a reasonable amount of experimental resources. We first compare the different criteria for typical settings and sort them according to their resilience to excess noise. Then, we introduce a further improvement to the Expectation Value Matrix method, which results in the desired optimal benchmark criterion. Finally, we investigate naturally occurring phase fluctuations and find them to further simplify the implementation of our criterion. Thus, we formulate the first truly useful way of validating experiments for the quantum storage or transmission of light.