Fault tolerant controlled quantum dialogue against collective noise*

Abstract

Quantum system is inevitably affected by the external environment in the real world. Two controlled quantum dialogue protocols are put forward based on logical χ-type states under collective noise environment. One is against collective-dephasing noise, while the other is against collective-rotation noise. Compared with existing protocols, there exist several outstanding advantages in our proposed protocols: Firstly, the χ-type state is utilized as quantum channels, it possesses better entanglement properties than GHZ state, W state as well as cluster state, which make it difficult to be destroyed by local operations. Secondly, two kinds of logical χ-type states are constructed by us in theory, which can be perfectly immune to the effects of collective noise. Thirdly, the controller can be offline after quantum distribution and permission announcement, without waiting for all the participants to complete the information coding. Fourthly, the security analysis illuminates that our protocols can not only be free from the information leakage, but also resist against the intercept-and-resend attack, the entanglement-and-measure attack, the modification attack, the conspiring attack, and especially the dishonest controller’s attacks.

Quantum Dialogue Protocols: A Review

“…Since the quantum channels are prone to noise, it's unavoidable. So, in 2020, to eradicate the disruption from the surrounding factors, Chang [29] designed a CQD protocol against collective noise, which are against collective-dephasing noise and collective-rotation noise, respectively, by employing decoherence-free states, e.g., -type entangled state. Especially, it needs to emphasize that not only are two types of logical χtype states generated by them, in theory, to be against collective noise, but their protocols can effectively withstand both the conspiring assault and the dishonest controller's assaults.…”

Quantifying entanglement in terms of an operational way*

“…( 1) can be replaced by its subset Q(ρ) ⊂ L(ρ), where Q(ρ) covers all the pure states |φ satisfying Eq. (10). Theorem 1 has provided us with an operational way to define an entanglement monotone from a pure-state entanglement monotone F. That is, the entanglement of a state ρ quantifies the least entanglement of the pure states which can be converted into ρ.…”

“…Entanglement is one of the most intriguing quantum features [1,2] and plays an important role in many quantum information processing tasks, [3,4] so quantum entanglement has been recognized as a key physical resource in quantum information. [5][6][7][8][9][10][11][12] Quantification of entanglement, triggering the various researches on the quantum resource theory, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] has attracted wide interest for several decades. However, quite limited progress has been made up to date, due to the good understanding of entanglement only restricted to bipartite pure states and low-dimensional mixed states.…”

Development of Quantum Private Queries Protocol on Collective-Dephasing Noise Channel

“…With the change of collective-dephasing noise [12][13][14][15], the horizontally polarized state of a photon |0 will remain, the vertically polarized state of a photon |1 will be turned into e iϕ |1 , that ϕ is the parameter of the collective-dephasing noise changing with time. Two logical qubits are defined as |0 dp = |01 and |1 dp = |10 , they can resist the collective-dephasing noise [16].…”