Relation Between Purity of an Open Qubit Dynamics and Its Initial Correlation with an Environment

Purity as a quantifier of an impact of environment on an open quantum system is studied for a qubit dephasingly interacting with its environment. We analyze how time evolution of the purity depends on initial states of the composite system both in the case of infinite and finite environments. It is shown that for a certain class of initial preparations, the purity of an evolving qubit state initially correlated with infinite environment can be greater than in the case of uncorrelated qubit-environment initial preparations. We identify a class of initial states leading to such desired outcome.     

Dynamics of Multi-Level Open Quantum Systems with Initial System-Environment Correlations

Physics of Particles and Nuclei Letters - Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level open quantum...     

On the Geometric Distance Between Quantum States with Positive Partial Transposition and Private States

We prove an analytic positive lower bound for the geometric distance between entangled positive partial transpose (PPT) states of a broad class and any private state that delivers one secure key bit. Our proof holds for any Hilbert space of finite dimension. Although our result is proven for a specific class of PPT states, we show that our bound nonetheless holds for all known entangled PPT states with non-zero distillable key rates, irrespective of whether they are in our special class or not. Thus, our result naturally leads to the conjecture of impossibility of using PPT-bound entangled state in physical implementation of quantum key distribution.     

Optimal Estimation of Qubit States with Continuous Time Measurements

We propose an adaptive, two step strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local minimax optimality means that given n identical qubits, there exists no estimator which can perform better than the proposed estimator on a neighborhood of size n ^−1/2 of an arbitrary state. In particular, it is asymptotically Bayesian optimal for a large class of prior distributions. We present a physical implementation of the optimal estimation strategy based on continuous time measurements in a field that couples with the qubits. The crucial ingredient of the result is the concept of local asymptotic normality (or LAN) for qubits. This means that, for large n, the statistical model described by n identically prepared qubits is locally equivalent to a model with only a classical Gaussian distribution and a Gaussian state of a quantum harmonic oscillator. The term ‘local’ refers to a shrinking neighborhood around a fixed state ρ ₀. An essential result is that the neighborhood radius can be chosen arbitrarily close to n ^−1/4. This allows us to use a two step procedure by which we first localize the state within a smaller neighborhood of radius n ^−1/2+ϵ, and then use LAN to perform optimal estimation.     

Wigner Functions and Spin Tomograms for Qubit States

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel connecting Wigner symbols on the discrete phase space with the tomographic symbols.     

Two-Photon Two-Focus Fluorescence Correlation Spectroscopy with a Tunable Distance Between the Excitation Volumes

In the present work, a Michelson interferometer was combined with a two-photon excitation microscope to perform two-focus Fluorescence Correlation Spectroscopy. This simple and original approach allows us to tune the distance between the two excitation volumes and determine absolute diffusion constants. The technique was validated on different model systems that demonstrate the sensitivity of the approach.     

Entanglement Dynamics Between Two Atoms Within Different W-like Initial States

We investigate the entanglement dynamics between two atoms which are trapped in an optical cavity with the help of the concurrence and the negativity for two different kinds of normalized W-like initial states. The results show that one of them can suffer the so-called entanglement sudden death (ESD) depending on parameters of the initial state when the optical cavity in the vacuum state, while the other one does not for whatever parameters. However when the initial optical cavity photon number is nonzero, no matter what W-like state as atoms’ initial state, the atoms’ subsystem always undergoes the ESD phenomenon. Meanwhile, by comparing concurrence with negativity, we find that our model gives a concrete example to support the conclusions in the previous reference.     

Locally Performing an Inner Product Modification on Remote Qubit Product States via Partially Entangled Qubit Pairs

We give a scheme for locally implementing an inner product modification onto remote qubit product states using partially entangled states, which is designed for obtaining conclusive result with optimal success probability. We exemplify this remote inner product modification (RIPM) by applying it to two-qubit product states via three partially entangled qubit pairs and, additionally, we construct a quantum network to implement this RIPM. It is interesting that our treatment can save entanglement resources.     

Geometry of Quantum Coherence for Two Qubit X States

The geometry of the structure of entanglement and discord for Bell-diagonal states is depicted by Lang and Caves (Phys. Rev. Lett. 105, 150501, 2010). In this paper, we investigate the geometry with respect to several distance-based quantifiers of coherence for Bell-diagonal states. We find that as both l₁ norm and relative entropy of coherence vary continuously from zero to one, their related geometric surfaces move from the region of separable states to the region of entangled states, a fact illustrating intuitively that quantum states with nonzero coherence can be used for entanglement creation. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equals to its relative entropy of coherence, and depict the surfaces related to the equality. We give surfaces of relative entropy of coherence for X states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherences under local nondissipative channels decrease.

     

Superposition Principle for Qubit States in the Spin-Projection Mean Representation

Journal of Russian Laser Research - We formulate the superposition principle of two states of qubit as a nonlinear addition rule of mean values of spin projections onto three perpendicular...     

Improvement on Quantum Teleportation of Three and Four Qubit States Using Multi-Qubit Cluster States

International Journal of Theoretical Physics - In 2016, Li et al. [Int. J. Theor. Phys. 55, 1820–1823 (2016)] proposed schemes for quantum teleportation of certain class of three and four...     

Quantum Zeno Effect with Mixed Initial States

Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This shows the existence of Quantum Zeno effect in the system with mixed initial states.     

Multi-Hop Teleportation of an Unknown Qubit State Based on W States

Quantum teleportation is important in quantum communication networks. Considering that quantum state information is also transmitted between two distant nodes, intermediated nodes are employed and two multi-hop teleportation protocols based on W state are proposed. One is hop-by-hop teleportation protocol and the other is the improved multi-hop teleportation protocol with centralized unitary transformation. In hop-by-hop protocol, the transmitted quantum state needs to be recovered at every node on the route. In improved multi-hop teleportation protocol with centralized unitary transformation, intermediate nodes need not to recover the transmitted quantum state. Compared to the hop-by-hop protocol, the improved protocol can reduce the transmission delay and improve the transmission efficiency.     

Quantum Entanglement and Correlation of Two Qubit Atoms Interacting with the Coherent State Optical Field

International Journal of Theoretical Physics - Using the three criterions of the concurrence, the negative eigenvalue and the geometric quantum discord, we investigate the quantum entanglement and...     

Probabilistic Teleportation of a Single Qubit: Unearthing New W-Class of States

Journal of Experimental and Theoretical Physics - In this work, we propose a probabilistic teleportation protocol to teleport a single qubit via three-qubit W-states using two-qubit measurement...     

Tomography of Qubit States and Implementation of Quantum Algorithms by Unipolar Pulses

Journal of Experimental and Theoretical Physics - The conventional technique for controlling the states of individual qubits and quantum registers is based on the use of high-frequency modulated...     

Purity and Correlation of a Cavity Field Interacting with a SC Charge Qubit with a Lossy Cavity

A single-mode microwave cavity field, coupled to its reservoir, interacting generally with a superconducting charge qubit is considered. Using a certain canonical transformation for the qubit states, the system is transformed into the usual Jaynes-Cummings model. The solution of the master equation of this system, in the case of a high-Q cavity is obtained. The temporal evolution of the population inversion is explored. The effects of cavity damping on the purity of the qubit, the field and the global system state are studied. It is found that due to the coupling between the system and environment, the purity is lost. The entanglement is compared with total correlation. It is found that, with the damping parameter, the asymptotic value of the correlation measure is not null, since the global system evolves to a classically correlated state. The negativity is used as an indicator of the degree of entanglement between the qubit and the field. The results indicate the sensitivity of these aspects to change of the damping parameter.