Measurement-Induced Coherent Control of Non-Gaussian Operations on
Quantum State Preparation
TANG Xubing
1,2
, GAO Fang
1
, WANG Yaoxiong
1
, SHUANG Feng
1
*
1. Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei 230031, China
E-mail: fshuang@iim.ac.cn
2. Department of Mathematics & Physics, Anhui University of Technology, Ma’anshan 243032, China
E-mail: ttxxbb@ahut.edu.cn
Abstract: Quantum state preparation is an essential ingredient in quantum information processing. In this letter, based on
quantum coherent control induced by Bell measurement, non-Gaussian operations, namely adding (subtracting) one single
photon to (from) Gaussian-like input signal field, has been implemented to generate a single-photon-added and -subtracted
coherent (SPASC) superposition state. In order to carry out the coherent control, a specified conceptual experiment apparatus has
been proposed. By adjusting beamsplitter reflectivity and parameter gain of Ȥ(2) nonlinear crystal, the ingredients of this
superposition state can be manipulated. With the help of quasi-probability distribution Wigner function, the evolution of
non-classical properties with two controllable parameters can be visualized for this superposition state. The results show a
quantum non-Gaussian superposition state can be generated by the measurement-induced coherent control scheme.
Key Words: coherent control, non-Gaussian operations, Bell measurement, non-classical
1 Introduction
Despite the fact that the novel features of quantum system
is so attractive, it is very difficult to engineer its dynamics
due to its extremely short dynamic time scale. Recently,
significant progress has been made in extending traditional
control theory to analyze quantum systems [1-3] and
experimentally demonstrate quantum coherent control [4-7].
As is known, it is inevitable to affect another part of
entangled multi-body quantum systems when one is trying
to manipulate a subsystem. This kind of special correlation
gives us some hints about a specified control strategy to
design a faithful quantum controller and actuator. Recent
developments of measurement-induced quantum coherent
control have taught us something about systematic
approaches to quantum control design and the qualitative
role of quantum coherence and entanglement between the
plant and controller in a feedback loop[8-10]. This paper
will propose another specific application of quantum
coherent control based on quantum measurement.
Quantum state can be employed as carrier of quantum bit
or qubit, and how to generate it accurately and steadily is a
very great important and indispensable step on the road of
practical quantum information processing. Especially for
the non-Gaussian quantum superposition state, its
generation attracts more and more attentions and various
control strategies have been proposed [8-17], such as
arbitrary superposition of zero- and one- photon [18], odd
photon number superposition state [18], the Schrödinger cat
state [10,12,16,17,20]. In Ref. [21], by preparing an
intermediate between a single-photon Fock state (fully
quantum mechanical) and a coherent (classical) one, the
*
This work is supported by National Natural Science Foundation of
China (NSFC) (No. 61203061; 61074052); Foundation of the President of
Hefei Institutes of Physical Science CAS; and also supported by
Outstanding Young Talent Foundation of Anhui Province Colleges and
Universities No.2012SQRL040; Natural Science Foundation of Anhui
Province Colleges & Universities under grant KJ2012Z035.
author offers an opportunity to closely follow the smooth
transition between the particle-like and wave-like behavior
of light. It must be very interesting if similar situation
happens between the discrete variable (DV) superposition
states and the continuous variable (CV) superposition
coherent states.
In this letter, based on quantum coherent control induced
by Bell measurement, we implement non-Gaussian
operations, namely adding (subtracting) one single photon
to (from) Gaussian-like input signal field to generate a
single-photon-added and -subtracted coherent (SPASC)
superposition state. On the one hand, this state can give us a
further understanding of such a smooth transition between
the superposition of non-classical optical fields and that of
coherent states. The latter is considered to be most close to
the classical state. Moreover, non-Gaussian operations, as
the results of conditional local subtraction of one single
photon or two photons from the Gaussian entangled state,
can improve the Gaussian-like entanglement [22].
Considering the absence of strong nonlinear interactions
[23,24] or photon number resolving detectors [25], we
utilized nonlinear crystal (e.g. type-I beta-barium borate
(BBO) crystal) and simple optical elements (e.g. high
transmission beamsplitter, HT-BS) to generate the SPASC
superposition state. If input coherent field is weak (ΊĮΊ<
3), HT-BS and nonlinear crystal just annihilate and create
one single photon, respectively. Starting from this point of
view, we arrange our work as following: In Sec. II, we
briefly introduce the realization of non-Gaussian operators
relied on the simple optical elements. In Sec. III, we propose
a conceptual experiment apparatus to implement a
measurement-induced coherent control strategy for
generating the SPASC superposition state. In Sec. IV,
employing the quasi-probability distribution Wigner
function, we visualize the probability distribution of this
superposition state and manipulate its non-classical features
with two specified parameters.
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