The effect of quantum noise on the restricted quantum game

It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of 0 〈 p ≤ 0.422 （p is the quantum noise parameter）, while two special Nash equilibria appear in the range of 0.422 〈 p 〈 1. The advantage that the quantum player diminished only in the limit of maximum quantum noise. Increasing the amount of quantum noise leads to the increase of the classical player＇s payoff and the reduction of the quantum player＇s payoff, but is helpful in forming two Nash equilibria.     

Property of Quantum Correlations with Correlated Noise

We analyze the classical and quantum correlation properties of the standard and so-called quasiclassical depolarizing channel with correlated noise and non-Markovian dephasing channel, specifically we use the quantum discord, entanglement, and measurement-induced disturbance （MID） to measure the quantum correlations. For the depolarizing channel, we find that the memory effect has more influence on the MID and quantum discord than entanglement. For the dephasing channel, we show that the non-Markovian dephasing channel is more robust than Markovian dephasing channel against deeoherence. We also find that at first MID and quantum discord take different values, and then after a specific time they will take almost the same value and both decay monotonically in the same way.     

Quantum Model of Bertrand Duopoly

We present a quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we find only one Nash equilibirum point for the maximally entangled initial state. The presence of quantum entanglement in the initial state gives payoffs higher to the firms than the classical payoffs at the Nash equilibrium. As a result, the dilemma-like situation in the classical game is resolved.     

Controlling quantum discord dynamics in cavity QED systems by applying a classical driving field with phase decoherence

We investigate a two-level atom interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence and find that a stationary quantum discord can arise in the interaction of the atom and cavity field as the time turns to infinity.We also find that the stationary quantum discord can be increased by applying a classical driving field.Furthermore,we explore the quantum discord dynamics of two identical non-interacting two-level atoms independently interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence.Results show that the quantum discord between two atoms is more robust than entanglement under phase decoherence and the classical driving field can help to improve the amount of quantum discord of the two atoms.     

Entanglement Preserving in Quantum Copying of Three－Qubit Entangled State

We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes,respectively,and investigate iterating quantum copying for the three-qubit system.There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine.we also show that the inter-two-qubit entanglement is preserved better than the inter-three-qubit entanglement in the local cloning process.We find that non-local cloning is much more efficient than the local copying for broadcasting entanglement,and output state via non-local cloning exhiits the fidelity better than local cloning.     

The quantum spectra analysis of the circular billiards in wells

We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.     

Quantum Spectra and Classical Orbits in Two-Dimensional Equilateral Triangular Billiards

We study the correspondence between quantum spectra and classical orbits in the equilateral triangular billiards. The eigenstates of such systems are not separable functions of two variables even though the problem is exactly solvable. We calculate the Fourier transform of a quantum spectral function and find that the positions of the peaks match well with the lengths of the classical orbits. This is another example showing that the quantum spectral function provides a bridge between quantum and classical mechanics.     

The effect of quantum noise on multiplayer quantum game

It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of 0≤p≤0.622 （p is the quantum noise parameter）, and then disappears in the range of 0.622 〈 p≤ 1. Increasing the amount of quantum noise leads to the reduction of the quantum player＇s payoff.     

A Scheme for Dense Coding in the Non-Symmetric Quantum Channel

We investigate the dense coding in the case of non-symmetric Hilbert spaces of the sender and receiver‘s particles sharing the quantum maximally entangled state. The efficiency of gaining classical information is also considered.We conclude that when a more level particle is with the sender, she can obtain a non-symmetric quantum channel from a symmetric one by entanglement transfer. Thus the efficiency of information transmission is improved.     

Quantum Algorithms for Some Well—Known NP Problems

It is known that quantum computer is more powerful than classical computer.In this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least quadratically faster than the classical ones.     

Quantum correlation of a three-particle W-class state under quantum decoherence

We investigate the quantum characteristics of a three-particle W-class state and reveal the relationship between quan- tum discord and quantum entanglement under decoherence. We can also identify the state for which discord takes a maximal value for a given decoherence factor, and present a strong bound on quantum entanglement-quantum discord. In contrast, a striking result will be obtained that the quantum discord is not always stronger than the entanglement of formation in the case of decoherence. Furthermore, we also theoretically study the variation trend of the monogamy of quantum correlations for the three-particle W-class state under the phase flip channel, and find that the three-particle W-class state could transform from polygamous into monogamous, owing to the decoherence.     

Investigations into quantum correlation of coupled qubits in a squeezed vacuum reservoir

In this paper,we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in a squeezed vacuum reservoir.We compare and analyze the effects of squeezed parameters on quantum discord and quantum concurrence.The results show that in a squeezed vacuum reservoir,the quantum discord and quantum concurrence perform with completely opposite behaviors with the change of squeezed parameters.Quantum discord survives longer with the increase of squeezed amplitude parameter,but entanglement death is faster on the contrary.The results also indicate that the classical correlation of the system is smaller than quantum discord in a vacuum reservoir,while it is bigger than quantum discord in a squeezed vacuum reservoir.The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments,which indicates that the entanglement actually is easily affected by decoherence and quantum discord has a stronger ability to avoid decoherence in a squeezed vacuum reservoir.     

Compare Quantum Operation Sensitivity for Different Distance Measures

In this paper, we compare the quantum operation sensitivity for different distance measures. We find that, among all usual distance measures, Bures fidelity is more sensitive to quantum operation than others. This may explain in some sense why fidelity is so useful in quantum information theory.     

The Squeezing Effect in a Mesoscopic RLC Circuit

Using the path integral method we derive quantum wave function and quantum fluctuation 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.     

An Intuitive Expression for Inseparability Condition of a Two-Mode Squeezed Vacuum State in a Thermal Environment

Considering the propagation of a two-mode optical field that is initially in a squeezed vacuum state in a thermalenvironment, we obtain an intuitive expression for inseparability condition of the two-mode mixed state which isgiven in the coherent state representation. This condition shows that the two modes have quantum entanglementif and only if the coefficient of the correlation term between the two modes is larger than that of the off-diagonalterm of each mode in the density matrix. We find that even if the quantum channel is dynamically coupled to thethermal environment, the fidelity for teleporting coherent states larger than 1/2 is still the criterion for quantum teleportation. We also show that the entanglement, squeezing and quantum teleportation conditions are alwaysconsistent with each other.     

Quantum Dense Coding in Multiparticle Entangled States via Local Measurements

We study quantum dense coding between two arbitrarily fixed particles in a (N 2)-particle maxlmally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted classical information amount through such an entangled quantum channel is usually less than two classical bits. However, the information amount may reach two classical bits of information, and the classical information capacity is independent of the number of the entangled particles under certain conditions. The results offer deeper insight into quantum dense coding via quantum channels of multi-particle entangled states.     

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time,we find that when Nasli equilibrium exists the payoff function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example showing quantum game and classical game may differ.When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.     

A hybrid quantum encoding algorithm of vector quantization for image compression

Many classical encoding algorithms of vector quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45\sqrt{N} times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than \sqrt{N} for most images, and it is more efficient than the pure quantum algorithm.     

Unknowability of Quantum State forbids perfectly quantum operations

We analyze the oonnection between quantum operations and accessible information. And we find that the accessible information decreases under quantum operations. We show that it is impossible to perfectly manipulate an unknown state in an open quantum system. That the accessible information decreases under quantum operations gives a fundamental limitation in the microscopic world.     

Quantum Monty Hall Problem under Decoherence

We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing, and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice＇s quantum strategy. Whereas in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, Bob＇s payoffs are found symmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob＇s classical strategy remains always dominant against any choice of Alice＇s strategy.