Maps of Matrices and Portrait Maps of the Density Operators of Composite and Noncomposite Systems

We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary N × N matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. The structure of the maps is inspired by “portrait” map of the probability vectors corresponding to the action on the vectors by stochastic matrices containing either unity or zero matrix elements. We obtain new entropic inequalities for arbitrary qudit states including a single qudit and discuss entangled single qudit state. We consider in detail the examples of N = 3 and 4. Also we point out the possible use of entangled states of systems without subsystems (e.g., a single qudit) as a resource for quantum computations.     

Tomographic and Improved Subadditivity Conditions for Two Qubits and a Qudit with j = 3/2

We obtain a new entropic inequality for quantum and tomographic Shannon information for systems of two qubits. We derive the inequality relating quantum information and spin-tomographic information for particles with spin j = 3/2. We recommend the method for obtaining new entropic and information inequalities for composite systems of qudits, as well as for one qudit.     

Inequalities for nonnegative numbers and information properties of qudit tomograms

We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize the degree of quantum correlations in addition to noncontextuality and quantum discord. We use the subadditivity and strong subadditivity conditions for qudit tomographic-probability distributions depending on the unitary-group parameters in order to derive new inequalities for Shannon, Rényi, and Tsallis entropies of spin states.     

Inequalities for Purity Parameters of Multiqudit and Single-Qudit States

We analyze the recently found inequality for eigenvalues of the density matrix and purity parameters describing either a bipartite-system state or a single-qudit state. We rewrite the Minkowski-type trace inequality for the density matrices of the qudit states in terms of the purity parameters and discuss the properties of the inequality obtained, paying special attention to the X-states of two qubits and a single qudit. Also we study the relation of the purity inequalities obtained with the entanglement.     

Deformed Subadditivity Condition for Qudit States and Hybrid Positive Maps

We extend the subadditivity condition for q-deformed entropy of a bipartite quantum system to the case of an arbitrary quantum system including the single qudit state. We present the subadditivity condition for the density matrix of the single qutrit state in an explicit form. We obtain the inequality for the purity parameters of a bipartite quantum system and its subsystems. We propose a positive map construction using the fiducial density matrix.     

New Inequality for Density Matrices of Single Qudit States

Using the monotonicity of relative entropy of composite quantum systems, we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Examples of qutrit state inequalities and the “qubit portrait” bound for the distance between the qutrit states are considered in explicit form.     

Entropic and Information Inequalities for Indivisible Qudit Systems<Superscript>*</Superscript>

We present the idea that in both classical and quantum systems all correlations available for composite multipartite systems, e.g., bipartite systems, exist as “hidden correlations” in indivisible (noncomposite) systems. The presence of correlations is expressed by entropic-information inequalities known for composite systems like the subadditivity condition. We show that the mathematically identical subadditivity condition and the mutual information nonnegativity are available as well for noncomposite systems like a single-qudit state. We demonstrate an explicit form of the subadditivity condition for a qudit with j = 2 or the five-level atom. We consider the possibility to check the subadditivity condition (entropic inequality) in experiments where such a system is realized by the superconducting circuit based on Josephson-junction devices.     

Generalized Qubit Portrait of the Qutrit-State Density Matrix

We obtain new inequalities for tomographic probability distributions and density matrices of qutrit states by generalization of the qubit-portrait method. We propose an approach based on the quditportrait method of obtaining new entropic inequalities. Our approach can be applied to the case of arbitrary nonnegative hermitian matrices, including the density matrices of multipartite qudit states.     

Subadditivity Condition for Spin Tomograms and Density Matrices of Arbitrary Composite and Noncomposite Qudit Systems

We obtain a new quantum entropic inequality for the states of a system of n ≥ 1 qudits. The inequality has the form of the quantum subadditivity condition of a bipartite qudit system and coincides with the subadditivity condition for the system of two qudits. We formulate a general statement on the existence of the subadditivity condition for an arbitrary probability distribution and an arbitrary qudit-system tomogram. We discuss the nonlinear quantum channels creating the entangled states from separable states.     

Spin-rotation and hfs constants for the X2Σ+ and B2Σ+ states of CaI

The molecular-beam, laser-rf double-resonance technique is used to obtain precise values for the spin-rotation and hyperfine interaction constants in the X²Σ⁺ ground state of ⁴⁰Ca¹²⁷I. The measured X-state splitting information is supplemented by BX optical hfs splitting data to obtain hfs constants for the excited B²Σ⁺ state. The results for both states are compared with previously reported values for CaI and other calcium monohalides.     

弱测量对四个量子比特量子态的保护

廖湘萍等(Chin.Phys.B 23 020304,2014)指出弱测量和弱测量反转操作可以保护三个量子比特的纠缠,提高保真度.本文将弱测量方法推广至四个量子比特的情况,研究了几种典型四个量子比特量子态的演化.结果表明:在振幅阻尼通道中,弱测量方法能够有效地提高系统量子态的保真度.分析了影响量子态保真度的各种因素,对比了不同量子态的演化特征,划分了量子态保真度提高的敏感区域.最后,对弱测量方法抑制量子态衰减的内在机制做了合理的物理解释.     

Higher-Order Nonclassicality in Photon Added and Subtracted Qudit States

Higher-order nonclassical properties of r photon added and t photon subtracted qudit states (referred to as rPAQS and tPSQS, respectively) are investigated here to answer: How addition and subtraction of photon can be used to engineer higher-order nonclassical properties of qudit states? To obtain the answer, higher-order moment of relevant bosonic field operators is first obtained and subsequently used to study the higher-order nonclassical properties (e.g., higher-order antibunching, higher-order squeezing, and higher-order sub-Poissonian photon statistics) of the corresponding states. These witnesses establish that rPAQS and tPSQS are highly nonclassical. To quantitatively establish this observation and to make a comparison between rPAQS and tPSQS, volumes of the negative part of Wigner function are computed. Finally, for the sake of verifiability of the obtained results, optical tomograms are also reported. Throughout the study, a particular type of qudit state named as a new generalized binomial state is used as an example.     

Standard form of qudit stabilizer groups

We investigate stabilizer codes with carrier qudits of equal dimension D, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding stabilizer, and this implies that the code and its stabilizer are dual to each other. We also show that any qudit stabilizer can be put in a canonical, or standard, form using a series of Clifford gates, and we provide an explicit efficient algorithm for doing this. Our work generalizes known results that were valid only for prime dimensional systems and may be useful in constructing efficient encoding/decoding quantum circuits for qudit stabilizer codes and better qudit quantum error correcting codes.     

Subadditivity and Strong Subadditivity Conditions for the Density Matrix of the Five-Level Atom

We obtain new quantum inequalities for von Neumann entropy of the five-level atom, which are analogs of the subadditivity condition known for bipartite quantum systems and the strong subadditivity condition known for tripartite quantum systems. We discuss the possibility to check the inequalities for the single qudit with j = 2, which can be realized as a five-level atom in the experiments with superconducting circuits. We present the strong subadditivity conditions for the finite-level atomic populations.     

Concurrence and Negativity as a Family of Two Measures Elaborated for Pure Qudit States

We investigate entangled states of an atomic trapped ion interacting with two phonons in the Λ configuration forming a twelve-dimensional Hilbert space. We study two elaborated measures, namely, the concurrence C and negativity N, which are important in current theoretical studies. Therefore, we work with the three-dimensional reduced density matrix in calculating the measures elaborated for pure qudit states in the ionic–phononic system. To demonstrate the benefits of the family of the two measures elaborated, we perform the calculations for different values of the Lamb–Dicke (LD) parameter η = 0.01, 0.3, and 0.5. Finally, we show that the pure qudit states under study are maximum entangled states.     

Planck-scale corrections to Friedmann equation

Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.     

Optimal probabilistic teleportation of an unknown N-level qudit via information extraction

In this Letter, we consider the optimal probabilistic teleportation in N-level qudit via information extraction. We also argue that the purification scheme via entanglement swapping cannot achieve optimal efficiency in N-qubit case when N is larger than 2.     

On the energy of ions at the expansion of a hot plasma layer into vacuum

We re-examine one-pion exchange as a possible binding mechanism in the X (3872) charmonium-like state and argue it to be not sufficiently binding for this purpose. We conclude therefore that other short-range dynamics are responsible for the X formation.     

Generalized tripartite scheme for sharing arbitrary 2n-qudit state

Utilizing three non-maximally entangled qutrit pairs as quantum channels, we first propose a generalized tripartite scheme for sharing an arbitrary two-qutrit state with generalized Bell-state measurements. In the scheme if and only if the two recipients collaborate together, they can recover the split qutrit state with the probability determined uniquely by the smallest coefficients of the non-maximally entangled pairs. Afterwards, we further extend the scheme for sharing an arbitrary 2n-qudit state by taking 3n non-maximally entangled qudit pairs as quantum channels. Moreover, the scheme success probability relative to the inherent entanglement in quantum channels and its structure is simply discussed.     

Entanglement of Formation for Qubit-Qudit System Using Partition of Qudit System into a Set of Qubit System

Gerjuoy (Phys. Rev. A 67:052308, 2003) has derived a closed-form lower bound for the entanglement of formation of a mixed qubit-qudit system (qudit system has d levels with d≥3). In this paper, inspired by Gerjuoy’s method, we propose a scheme that partitions a qubit-qudit system into d(d?1)/2 qubit-qubit systems, which can be treated by all known methods pertinent to qubit-qubit system. The method is demonstrated by a qubit-qudit system (the levels of qudit are d=3 and d=5, respectively).