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Identification of performance parameter of a multi-level open quantum system is a central problem in a growing number of applications of information engineering. Based on the quantum tomography, this paper aims at finding a method for identifying reduced density matrix of open quantum system. State identification of open quantum system approaches is presented for two-level, three-level and N-level systems, respectively. The results show that not only the reduced density matrix can be reestablished, but also the quantum state information can be received in quantum tomography experiment.

Yu-Han Hu,1,* Shuai Ma,1,* Xiang-Nan Zhang,2 Zhe-Ying Zhang,1 Hui-Fang Zhu,1,2 Ying-Hua Ji,3 Jian Li,4 Xin-Lai Qian,1,2 Yong-Xia Wang1,2 1Department of Pathology, School of Basic Medical Sciences, Xinxiang Medical University, Xinxiang, Henan 453000, People’s Republic of China; 2Department of Pathology, The Third Affiliated Hospital of Xinxiang Medical University, Xinxiang, Henan 453000, People’s Republic of China; 3Department of Oncology, The First Affiliated Hospital of Xinxiang Medical University, Xinxiang, Henan 453000, People’s Republic of China; 4Department of Surgery, The First Affiliated Hospital of Xinxiang Medical University, Xinxiang, Henan 453000, People’s Republic of China*These authors contributed equally to this workCorrespondence: Yong-Xia Wang; Xin-Lai QianDepartment of Pathology, School of Basic Medical Sciences, Xinxiang Medical University, Xinxiang, Henan 453000, People’s Republic of ChinaTel +86-15090325842; +86-13839073820Email 58866999@qq.com; qxlfssws@163.comBackground: Colorectal cancer (CRC) is one of the most common malignancies worldwide. Studies have demonstrated that epigenetic modifications play essential roles in the development of CRC. ADHFE1 is a differentially expressed gene that has been reported to be hypermethylated in CRC. However, the role and mechanism of ADHFE1 in the proliferation of CRC remain unclear.Materials and methods: ADHFE1 expression was analyzed in CRC tissues by IHC and qRT-PCR, and the relationship between ADHFE1 expression and the clinicopathological parameters was analyzed. Cell proliferation were assessed by the in vitro and in vivo experimental models. GSEA assay was performed to explore the mechanism of ADHFE1 in the proliferation of CRC. Flow cytometry and Western blot were used to detect the activation of the cell cycle signaling. Bisulfite genomic sequence (BSP) assay was used to test the methylation degree of ADHFE1 gene promoter in CRC tissues.Results: Here, we verified that ADHFE1 was down-regulated and hypermethylated in CRC tissues. The down-regulation of ADHFE1 was correlated with poor differentiation and advanced TNM stage of CRC patients. And ADHFE1 expression restored when the CRC cell line SW620 was treated with the demethylating agent 5-Aza-CdR. Overexpression of ADHFE1 inhibited the proliferation of CRC, while ADHFE1 knockdown promoted the proliferation of CRC cells in vitro and in vivo. Moreover, ADHFE1 overexpression could induce a significant G1-S cell cycle arrest in CRC cells and vice versa.Conclusion: Hypermethylation of ADHFE1 might promote cell proliferation by modulating cell cycle progression in CRC, potentially providing a new therapeutic target for CRC patients.Keywords: ADHFE1, colorectal cancer, hypermethylation, proliferation, cell cycle

Dynamical evolutions of quantum correlations in circuit quantum electrodynamics (circuit-QED) are investigated under various dissipative modes. The influences of photon number, coupling strength, detuning and relative phase angle on quantum entanglement and quantum discord are compared as well. The results show that quantum discord may be less robust to decoherence than quantum entanglement since the death and revival also appears. Under certain dissipative mode, the decoherence subspace can be formed in circuit-QED due to the cooperative action of vacuum field. Whether a decoherence subspace can be formed not only depends on the form of quantum system but also relates closely to the dissipative mode of environment. One can manipulate decoherence through manipulating the correlation between environments, but the effect depends on the choice of initial quantum states and dissipative modes. Furthermore, we find that proper relative phase of initial quantum state provides one means of suppressing decoherence.

Utilizing the method of optimal control, we investigate the tactics of state transfer in the non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz–Drude regularization is numerically studied. Owing to the decoherence and memory effects of non-Markovian channel, the purity of quantum state attenuates damply in the free evolution. The numerical simulations indicate that arbitrary state transfer for non-Markovian system can be realized under the optimal control function by a proper external control field with a success rate of more than 98 percent. When the right control field and function is implemented, not only the decoherence is compensated completely but also the purity of quantum states are maintained in the process of state transfer.

A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single-qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.

Taking into account the interaction between electrons and phonons, in the case without-rotating-wave approximation, we study the entangling property between the mesoscopic circuit and environment at coherent state or equilibrium state. The result indicates that, in long time limit t → ∞, the averages of charge and current in the circuit only depend on the average of the system at the initial state when the environment is initially at thermal equilibrium. However, when the environment is initially at coherent state, the average of charge and current in the circuit is determined by the specific coherent state ensemble. Generally speaking, the entanglement between the circuit and environment will lead to the quantum state purity declining of the circuit, then the circuit emerges decoherent phenomenon, and so a mixed state appears. Purity changes are related to the initial quantum state of environment and circuit. With the further evolution of time, coherence will be gradually restored, but cannot return to 1.

This paper investigates the relationship between the speed of a quantum not gate and the asymmetry of the potential in an interactive system formed by a two-level RF-SQUID qubit and a classical microwave pulse. The RF-SQUID is characterized by an asymmetric double well potential which gives rise to diagonal matrix elements that describe the interaction of the SQUID with the microwave pulse. And the diagonal matrix elements account for the interaction of the microwave pulse with the SQUID. The results indicate that, when the angular frequency of the microwave field is chosen as near resonate with the transition |0〉 ↔ |1〉0, i.e. ω1 - ω0 ≈ ωm, (1) the gate speed is decided by three factors, the Rabi frequency, the difference of the diagonal matrix elements between the two levels, and the angular frequency of the applied microwave pulse ωm; (2) the gate speed descends when the asymmetry of the potential is considered.

Based on the information theory, we present a density matrix to discuss coherent and squeezed states in a mesoscopic LC circuit with time-dependent frequency. With the relevant operators included in the density matrix, a connection between the appearance of coherent and squeezed states is established, i.e., the quantum state evolution of the system is closely related to the initial state. Generally speaking, due to the effect of environment temperature, the mesoscopic LC circuit will evolve to a squeezed state when it initially lies in an excited state. In particular, at a low temperature, step changes of circuit parameters will result in a squeezed minimum uncertainty state if the resonance frequency remains the same after the change.

Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix ρ(q,q',β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.

We discuss the relationship between external magnetic field and persistent currents of three mesoscopic-coupled rings with charge discreteness. Through numerical calculation and analysis, it is found that the properties of the persistent currents depend on both external magnetic flux and coupled factors. The positive coupling between the rings will decrease the persistent currents when 0

Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for a non-dissipative distributed parameter circuit (a uniform transmission line). Quantum fluctuations of charge and current in the vacuum state are investigated by adopting the canonical transformation and unitary transformation method. Our results indicate that in distributed parameter circuits, quantum fluctuations, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.

The quantum theory of the mesoscopic RLC circuit and the condition for Coulomb blockade are given by using canonical quantization and a unitary transformation from the classical equation of motion. Our results show that there is a threshold voltage eT in the circuit. The threshold voltage is related not only to the junction capacitance and inductance, but also to the resistance of the circuit. Generally speaking, the larger the resistance, the larger the threshold voltage. This clarifies the phenomenon of the Coulomb blockade of the dissipative mesoscopic circuit.

Using the path integral method we derive quantum wave function and quantum fluctuations of charge and current in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely, the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit. If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also find that uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.

In this paper we consider the movement of an electron in the single electron tunnel process through a mesoscopic capacitor. The results show that, due to the Coulomb force, there is a threshold voltage Vt in the mesoscopic LC circuit. When the external voltage is lower than the threshold voltage, the tunnel current value is zero and the Coulomb blockade phenomenon arises. Furthermore, considering that the mesoscopic dimension is comparable to the coherence length in which charge carriers retain the phase remembrance, a weak coupling can be produced through the proximity effect of the normal metal electrons of both electrodes of a mesoscopic capacitor. By varying the external voltage, we can observe the Shapiro current step on the current-voltage characteristic curve of a mesoscopic LC circuit.

Taking into consideration the interactions between electrons and phonons, we have studied the temporal evolution of the average charge and current in a dissipative mesoscopic RLC circuit. Our results show that a mesoscopic RLC circuit can be treated as an interactive system between an electromagnetic harmonic oscillator and many lattice harmonic oscillators; this is called the bathing of the harmonic oscillators. The results also show that the quantum equation of motion of the linear mesoscopic RLC circuit is identical in form to its classical equation of motion, the only difference between them being their respective meanings. In order to thoroughly study the quantum properties of a dissipative mesoscopic circuit, we have to consider not only the electromagnetic energy of the circuit, but also the crystal lattice vibration energy and the interactive energy between electrons and phonons.

We study the quantum fluctuations of the charge and current of two L-C dissipative mesoscopic circuit with the mutual inductance in the vacuum state. Our results show that the system state will evolve to a squeezed coherent state under the effect of external source. We find that the squeezing amplitude parameter is relative to the parameters of circuit and the mutual-inductance coefficient in the existence of dissipation. When the circuit has no dissipation or there is complete coupling between two meshes, the squeezing amplitude parameter only depends on the capacitance's ratio.

A scheme is proposed to controll the decoherence of three-level rf-SQUID qubit with asymmetric potential by designing an external electric circuit for superconductive flux qubit. The results show that it may not only raise the gate speed but also extend decoherence time for a three-level structure.