Dynamical Properties of Some Statistical Quantities for a Quantum System in Generalized Negative Binomial States

We estimate the quantum state of a qubit and a quantized radiation field yielding a generalized negative binomial distribution (GNBD). We give an explicit form for various generalized negative binomial states associated to superposition, even, odd, and q-deformed states. We investigate the dynamical properties of the Mandel parameter as a quantifier of the statistical properties for the radiation field corresponding to its dynamics. We obtain the quantum Fisher information based on the estimation of the atomic state and compare it with the Mandel parameter for different instances of the GNBD. The link between the statistical quantities for different parameters of the GNBD is explored.     

Some New Properties of Quantum Correlations

Quantum coherence measures the correlation between different measurement results in a single-system, while entanglement and quantum discord measure the correlation among different subsystems in a multipartite system. In this paper, we focus on the relative entropy form of them, and obtain three new properties of them as follows: 1) General forms of maximally coherent states for the relative entropy coherence, 2) Linear monogamy of the relative entropy entanglement, and 3) Subadditivity of quantum discord. Here, the linear monogamy is defined as there is a small constant as the upper bound on the sum of the relative entropy entanglement in subsystems.     

Duality Quantum Computers and Quantum Operations

We present a mathematical theory for a new type of quantum computer called a duality quantum computer that is similar to one that has recently been proposed. We discuss the nonunitarity of certain circuits of a duality quantum computer. We then discuss the relevance of this work to quantum operations and their convexity theory. This discussion is based upon isomorphism theorems for completely positive maps.     

Quantum Ramp Secret Sharing Scheme and Quantum Operations

In order to improve the efficiency of quantum secret sharing, quantum ramp secret sharing schemes were proposed (Ogawa et al., Phys. Rev. A 72, 032318 [2005]), which had a trade-off between security and coding efficiency. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an intermediate set, which cannot fully reconstruct the secret. This paper revisits the size of a share in the quantum ramp secret scheme based on a relation between the quantum operations and the coherent information. We also propose an optimal quantum ramp secret sharing scheme.     

Ambiguous Discrimination of General Quantum Operations

We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.     

A Class of General Quantum Operations

In this paper, we study the fixed points sets of a class of general quantum operations. We show that under some conditions, the fixed points sets of this class of quantum operations are trivial. Finally, we offer a sufficient and necessary condition in a special setting to ensure the fixed points sets are non-trivial.     

Study of Some Properties of Two-Level Atom in Quantum Optics

With the concept of negative photon and the K-photon J C model, we investigate analytically the effect of virtual photon field on the collapse revival effect of atomic inversion and squeezing of atom, we find that there is a significant effect of virtual photon field on atomic inversion and squeezing of atom; with the one-photon model as an example, we find that the squeezing of atom occurs periodically, the time and times of squeezing are only related to the resonance frequency and the amplitude of squeezing related to coupling constant of atom field, mean photon number and resonance frequency; also we show that the effect of squeezing of atom does not exist within rotating wave approximation if K≥3. Taking the approach of nearest-neighboring spectrum in the quantum chaos field, we investigate the properties of energy spectrum in one-photon JC model and show that the integrable region,non-integrable region and transition region of this system can be illustrated by a phase diagram;also we discuss the influence of interaction of atoms on spectrum and Δ₃ statistics of adjacent energy levels, we find that the influence of interaction is little obvious in strong field but takes great important role in weak field.     

几类宏观量子态的内部结构及其压缩特性

谐振子,变形振子,非简谐振子以及变形非简谐振子湮没算符高次幂的正交归一本征态都具有奇偶结构形式.正是由于这种结构特点决定了它们振幅的高次幂压缩性质.     

量子Generalized Reed-Solomon码

构造出了一族量子纠错码，这族码具有参数［［n，n-2k，k+1］］_q，是q维量子系统上的码，q是任意素数的幂.这族码的最小距离达到了理论上限，因此，以码距来说，它是最优的.证明了当2≤n≤q或者q²-q+2≤n≤q²时，码都是存在的.     

A Generalized Quantum Theory

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lüders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate—the non-existence of third-order interference [third-order interference and its impossibility in quantum mechanics were discovered by Sorkin (Mod Phys Lett A 9:3119–3127, 1994)]. This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed.     

Generalized Quantum Two-Qutrit-State Splitting

A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed, where two nonmaximally-entangled three-qutrit states are taken as the quantum channel among three parties. With the sender＇s help, if and only if both receivers collaborate together, they can securely share the quantum state in a probabilistic way by introducing an ancilla qutrit and performing appropriate unitary operations. The relation between the success probability and coefficients characterizing the quantum channel is revealed. The security of the present scheme is analyzed and confirmed. Moreover, the generalization of the three-party scheme to more-party case is also sketched.     

Generalized Quantum Two-Qutrit-State Splitting

A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed, where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties. With the sender's help, if and only if both receivers collaborate together, they can securely share the quantum state in a probabilistic way by introducing an ancilla qutrit and performing appropriate unitary operations. The relation between the success probability and coefficients characterizing the quantum channel is revealed. The security of the present scheme is analyzed and confirmed. Moreover, the generalization of the three-party scheme to more-party case is also sketched.     

量子Generalized Reed-Solomon码

构造出了一族量子纠错码,这族码具有参数［［n,n-2k,k+1］］_q,是q维量子系统上的码,q是任意素数的幂.这族码的最小距离达到了理论上限,因此,以码距来说,它是最优的.证明了当2≤n≤q或者q²-q+2≤n≤q²时,码都是存在的. 关键词： 量子Generalized Reed-Solomon码 量子MDS码 量子纠错码 量子信息     

Allowable Generalized Quantum Gates

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.     

Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations

A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen’s hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen’s hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.     

Allowable Generalized Quantum Gates Using Nonlinear Quantum Optics

In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross- Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality control gate also can be constructed conveniently. The special quantum control gate could be realized easily in optical system by our current experimental technology.     

Generalized Multiparty Quantum Single-Qutrit-State Sharing

We present a three-party quantum single-qutrit-state sharing scheme with a non-maximally entangled three-qutrit state as the quantum channel. In the scheme, the sender’s secret quantum information (i.e., the single-qutrit state) is split in such a way that it can be probabilistically reconstructed through introducing an auxiliary qutrit and performing appropriate operations provided that the receivers both collaborate together. We work out the success probability and reveal the relation between the probability and the parameters characterizing the quantum channel. After this, we then briefly introduce the generalization of the three-party scheme to a more-party one.     

Endomorphisms of Quantum Generalized Weyl Algebras

We prove that every endomorphism of a simple quantum generalized Weyl algebra A over a commutative Laurent polynomial ring in one variable is an automorphism. This is achieved by obtaining an explicit classification of all endomorphisms of A. Our main result applies to minimal primitive factors of the quantized enveloping algebra \({U_q({\mathfrak{sl}}_2)}\) and certain minimal primitive quotients of the positive part of \({U_q({\mathfrak{so}}_5)}\) .