Quantum secure direct communication with hybrid entanglement

doi:10.1007/s11467-024-1396-5

Front. Phys.

2024, Vol. 19

Issue (5) : 51201 https://doi.org/10.1007/s11467-024-1396-5

Quantum secure direct communication with hybrid entanglement

Peng Zhao^1,², Wei Zhong², Ming-Ming Du¹, Xi-Yun Li³, Lan Zhou³, Yu-Bo Sheng^1,²(

)

¹. College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China
². Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
³. College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

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Abstract

Quantum secure direct communication (QSDC) can transmit secret messages without keys, making it an important branch of quantum communication. We present a hybrid entanglement-based quantum secure direct communication (HE-QSDC) protocol with simple linear optical elements, combining the benefits of both continuous variables (CV) and discrete variables (DV) encoding. We analyze the security and find that the QSDC protocol has a positive security capacity when the bit error rate is less than 0.073. Compared with previous DV QSDC protocols, our protocol has higher communication efficiency due to performing nearly deterministic Bell-state measurement. On the other hand, compared with CV QSDC protocol, this protocol has higher fidelity with large $α$ . Based on these advantages, our protocol may provide an alternative approach to realize secure communication.

Keywords quantum secure direct communication hybrid entanglement, Bell-state measurement

Corresponding Author(s): Yu-Bo Sheng

About author:

^* These authors contributed equally.

Issue Date: 01 April 2024

Cite this article:

Peng Zhao,Wei Zhong,Ming-Ming Du, et al. Quantum secure direct communication with hybrid entanglement[J]. Front. Phys. , 2024, 19(5): 51201.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-024-1396-5
https://academic.hep.com.cn/fop/EN/Y2024/V19/I5/51201

Fig.1 Two Bell states measurement (BSM) elements in our protocol [51]. M1 is coherent state BSM element implemented by 50:50 beam splitter (BS) and two photon number parity detectors (PNPDs). It can unambiguously distinguish all four coherent Bell states with a high success rate

1 − e − 2 | α | 2

. The measurement fails only when no photon is detected at both PNPDs. M2 is BSM for polarized state with 50% success probability to discriminate two states

| ψ P ± ? = | H ? | V ? ± | V ? | H ?

. This measurement succeeds only when one detector from the upper two and another from the lower two detect a photon simultaneously.

	$\| ϕ + ? C$	$\| ϕ − ? C$	$\| ψ + ? C$	$\| ψ − ? C$

$\| ψ + ? P$	$\| Φ − ?$	$\| Φ + ?$	$∗$	$∗$
$\| ψ − ? P$	$∗$	$∗$	$\| Ψ − ?$	$\| Ψ + ?$
$F p$	$\| Φ + ?$	$\| Φ − ?$	$\| Ψ + ?$	$\| Ψ − ?$

Tab.1 The results for hybrid Bell states measurement (HBSM). The elements in the first row represent the four possible outcomes in the coherent BSM, while the first column stands for the two recognizable outcomes in the polarized BSM, with

F p

indicating a failure. The other cells in the table represent the HBSM outcomes, which are determined by the row and column that correspond to the coherent and polarized BSM results, respectively. The asterisk denotes combinations that are not possible or indicate a failure if one occurs.

Fig.2 Illustration for the HE-QSDC with a sequence of hybrid entangled photon pairs. The two particles that combine together represent a hybrid qubit and the two parts connected with a line are in a hybrid Bell entanglement. The smaller circles represent the polarization state and the larger circles represent the coherent state.

S M

represents message sequence and

S C

is check sequence.

Fig.3 Comparison of security capacity (bit rate) using Holevo bound (HE-QSDC) and entanglement distillation (ED-QSDC and ED-QKD). For simplicity, we assume that the reception rates of Bob (

Q B

) and Eve (

Q E

) are 0.8 and 1, respectively, as it is unlikely for Bob to have a count rate of 1 in practice and the count rate of Eve is not limited. It should be noted that ED-QSDC and ED-QKD do not have a deterministic BSM, so the key rate is multiplied by one half.

Fig.4 The fidelity of hybrid entanglement through lossy environment compared with CV entanglement according to different

α

. Hy (

α = 1

) represents the case of hybrid entanglement when

α = 1

, the same for Hy (

α = 2

) and Hy (

α = 5

). CV (

α = 1

) denotes the case of continuous variables entanglement when

α = 1

, the same for CV (

α = 2

) and CV (

α = 5

). The horizontal dashed lines means the classical limits 2/3.

r

represents normalization time, which includes interaction time

τ

and decoherence rate

γ

. Note that the fidelity of entanglement using CV is higher than that of hybrid entanglement for smaller

α

(such as

α = 1

). Conversely, for larger

α

(such as

α = 2

), the fidelity of using hybrid entanglement is higher than that of CV entanglement. As

α

continues to increase, the fidelity of both entanglements rapidly decreases in a very short time, causing the two curves to continuously converge.

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