Remote preparation and manipulation of squeezed light Dongmei Han12 Na Wang12 Meihong Wang12 Zhongzhong Qin12 Xiaolong Su12 1State Key Laboratory of Quantum Optics and Quantum Optics Devices

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Remote preparation and manipulation of squeezed light

Dongmei Han1,2, Na Wang1,2, Meihong Wang1,2, Zhongzhong Qin1,2, Xiaolong Su1,2∗

1State Key Laboratory of Quantum Optics and Quantum Optics Devices,

Institute of Opto-Electronics, Shanxi University,

Taiyuan, 030006, People’s Republic of China

2Collaborative Innovation Center of Extreme Optics, Shanxi University,

Taiyuan, Shanxi 030006, People’s Republic of China

Remote state preparation enables one to create and manipulate a quantum state based on the shared entan-

glement between distant nodes. Here, we experimentally demonstrate remote preparation and manipulation of

squeezed light. By performing homodyne projective measurement on one mode of the continuous variable en-

tangled state at Alice’s station, a squeezed state is created at Bob’s station. Moreover, rotation and displacement

operations are applied on the prepared squeezed state by changing the projective parameters on Alice’s state.

We also show that the remotely prepared squeezed state is robust against loss and N−1 squeezed states can

be remotely prepared based on a N-mode continuous variable Greenberger-Horne-Zeilinger-like state. Our re-

sults verify the entanglement-based model used in security analysis of quantum key distribution with continuous

variables and have potential application in remote quantum information processing.

I. INTRODUCTION

With the development of the quantum network, it becomes

possible for users who do not have the ability of preparing

quantum state to obtain a quantum resource and implement

quantum information processing. Remote state preparation

(RSP) enables one to create and manipulate quantum states re-

motely based on shared entanglement [1, 2]. Compared with

direct state transmission, where a prepared quantum state is

transmitted to the user through a quantum channel, RSP of-

fers remote control of the quantum state and intrinsic secu-

rity [3]. Compared with quantum teleportation, RSP does not

need joint measurement, requires fewer classical communi-

cation [4] and oﬀers the ability to manipulate quantum state

remotely. Based on RSP protocol, the single photon state

[5], sub-Poissonian state [6], superposition state up to two-

photon level [7], cat state [8], continuous variable qubits [9]

and squeezed state in the microwave regime [3] have been ex-

perimentally demonstrated.

A squeezed state has broad applications in continuous vari-

able (CV) quantum information [10–14], quantum measure-

ment [15, 16] and quantum-enhanced imaging [17, 18]. Up

to now, a squeezed state is prepared locally based on an op-

tical parametric ampliﬁer [19–23], four-wave mixing [24–26]

and a photonic chip [27, 28]. In addition to the local prepa-

ration, it has been proposed that a squeezed state can also

be prepared based on the RSP protocol by performing homo-

dyne measurement on one mode of a CV Einstein-Podolsky-

Rosen (EPR) entangle state [2]. This RSP protocol corre-

sponds to the entanglement-based model widely used in the

security analysis of CV quantum key distribution (QKD) [29–

32], where the security of CV QKD is analyzed based on a

CV EPR entangled state since it has been shown that CV QKD

with squeezed state (coherent state) is equivalent to homodyn-

ing (heterodyning) one mode of a EPR entangled state [29].

∗Electronic address: suxl@sxu.edu.cn

However, remote preparation and manipulation of squeezed

states by homodyne projective measurement have not been ex-

perimentally demonstrated.

Here, we experimentally demonstrate the remote prepara-

tion of squeezed states based on a CV EPR entangled state

distributed between Alice and Bob. By performing homodyne

projective measurement on Alice’s state, a squeezed state with

approximately −1.27 dB squeezing and ﬁdelity of 92% is re-

motely prepared at Bob’s station. Then, the prepared squeezed

state is rotated and displaced by changing the parameters

of the homodyne projective measurement at Alice’s station,

which is equivalent to performing rotation and displacement

operations on the squeezed state. We show that the remotely

prepared squeezed state is robust against loss in the quantum

channel. Furthermore, this scheme is extended to RSP based

on an N-mode CV Greenberger-Horne-Zeilinger-like (GHZ-

like) state Rdx|x,x,x, ..., xi, which is the eigenstate with total

momentum (phase quadrature) zero p1+p2+p3+... +pN=0

and relative positions (amplitude quadratures) xi−xj=0

(i,j=1,2,3, ...N) [33, 34], where N−1 squeezed states can be

remotely prepared simultaneously by performing homodyne

projective measurement on one mode of the CV GHZ-like

state. The presented results provide a new method to prepare

and manipulate squeezed states remotely.

II. REMOTE PREPARATION SCHEME

As shown in Fig. 1, a CV EPR entangled state is prepared

by a non-degenerate optical parametric ampliﬁer (NOPA) in a

quantum server and distributed to Alice and Bob through two

lossy channels. By measuring the phase quadrature of Alice’s

state and projecting the quadrature values to pA=0, a phase

squeezed state is prepared at Bob’s station remotely. By mea-

suring the amplitude quadrature of Alice’s state and projecting

the quadrature values to xA=0, the squeezed state is rotated

by 90 degrees, i.e. an amplitude squeezed state is prepared at

Bob’s station. The projective measurement is implemented by

the post-selection of quadrature values with a selection width

arXiv:2210.14418v1 [quant-ph] 26 Oct 2022

FIG. 1: Experimental set-up. Two modes of a CV EPR entangled

state are separated by a polarization beam splitter (PBS) and dis-

tributed to Alice and Bob respectively. Alice performs a homodyne

projective measurement on her mode. The phase-squeezed state or

amplitude-squeezed state is prepared at Bob’s station conditioned on

the measurement results of pA=0 or xA=0. A lossy channel is

simulated by the combination of a half-wave plate and a PBS. LO,

Local oscillator.

of |δx|<0.1. By projecting the quadrature values to xA=α

(pA=α), the displacement operation can be applied on the

remotely prepared squeezed states.

A CV EPR entangled state can be fully characterized by its

covariance matrix which is expressed by

σAB =





∆2ˆxA0∆2( ˆxAˆxB) 0

0∆2ˆpA0∆2( ˆpAˆpB)

∆2( ˆxBˆxA) 0 ∆2ˆxB0

0∆2( ˆpBˆpA) 0 ∆2ˆpB







,(1)

where ˆxA(B)=(ˆa†

A(B)+ˆaA(B))/√2 and ˆpA(B)=i(ˆa†

A(B)−

ˆaA(B))/√2 denote amplitude and phase operators where ˆa†,ˆa

are creation and annihilation operators respectively. We have

∆2ˆxA=∆2ˆpA=[ηA(Va+Vs)+(1 −ηA)]/2, ∆2ˆxB=∆2ˆpB=

[ηB(Va+Vs)+(1−ηB)]/2, and ∆2( ˆxAˆxB)=−√ηAηB(Vs−Va)/2,

∆2( ˆpAˆpB)=√ηAηB(Vs−Va)/2. Here, Vsand Varepresent

variances of squeezed and anti-squeezed quadratures, respec-

tively. We have VaVs=1/4 for a pure state and VaVs>1/4

for a mixed state. Additionally, ηAand ηBrepresent transmis-

sion eﬃciencies of Alice’s and Bob’s modes respectively. The

corresponding Wigner function of the CV EPR entangled state

is given by [12]

WAB(xA,pA,xB,pB)=1

√DetσABπ2exp (−1

2ξ>σ−1

ABξ),

(2)

where ˆ

ξ≡( ˆxA,ˆpA,ˆxB,ˆpB)>is the vector of the amplitude and

phase quadratures of the entangled state. The Wigner func-

tion of the homodyne projective measurement Πxon ampli-

tude quadrature of Alice’s state is expressed by [2]

W[Πx](xA)=δ(xA−α),(3)

where αis the projective value. After the Alice’s homodyne

projective measurement, Bob’s state is collapsed to

WB(xB,pB)=Z Z dxAdpAWAB ×W[Πx](xA).(4)

FIG. 2: (a), Quadrature values of Alice’s mode (70000 and 7000

for blue and red data points).(b), Quadrature values of Bob’s mode

(7000 data points).(c,d), Reconstructed Wigner functions of phase

and amplitude squeezed states. (e,f), Contour plots of phase and

amplitude-squeezed states displaced by (-0.01,0.17) and (0.20,0.05)

respectively in phase space. Around 10000 data points each are used

to reconstruct these Wigner functions.

For example, if Alice chooses xA=0 (α=0), Bob’s state be-

comes WB(xB,pB)=RdpAWAB(0,pA,xB,pB) which has unit

ﬁdelity with an ideal amplitude-squeezed state if the entan-

gled state is pure. Similarly, homodyne projective measure-

ment Πpon phase quadrature projects Bob’s mode to a phase-

squeezed state. Furthermore, for a CV EPR entangled state

with correlated amplitude and anti-correlated phase quadra-

tures in the case of inﬁnite squeezing, the projective measure-

ment of xA=αleads to an amplitude squeezed state displaced

by (α, 0) in phase space at Bob’s station [29]. Similarly, by

projecting on pA=α, a phase squeezed state displaced by (0,

−α) can be prepared.

III. EXPERIMENTAL SETUP AND RESULTS

In our experiment, the NOPA is composed by a 10-mm-

long α-cut type-II potassium titanyl phosphate (KTP) crystal

and a concave mirror with 50-mm radius. The front face of

the KTP crystal is coated to be used for the input coupler and

the concave mirror serves as the output coupler of the NOPA.

The details of parameters of the NOPA have been provided

elsewhere [35–37]. Our NOPA cavity is locked by using the

Lock-and-hold technique (See Appendix A for details). The

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RemotepreparationandmanipulationofsqueezedlightDongmeiHan1;2,NaWang1;2,MeihongWang1;2,ZhongzhongQin1;2,XiaolongSu1;21StateKeyLaboratoryofQuantumOpticsandQuantumOpticsDevices,InstituteofOpto-Electronics,ShanxiUniversity,Taiyuan,030006,People'sRepublicofChina2CollaborativeInnovationCenterofExtremeOpt...

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Remote preparation and manipulation of squeezed light Dongmei Han12 Na Wang12 Meihong Wang12 Zhongzhong Qin12 Xiaolong Su12 1State Key Laboratory of Quantum Optics and Quantum Optics Devices

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