Pair Of Qubits Research Articles

Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ 0〉 = cos α | 10〉 + sin α | 01〉 and | ϕ 0〉 = cos α | 11〉 + sin α | 00〉 cover three-dimensional surfaces in the diagram C ij × C ik × C il , where C mn stands for the concurrence between qubits m and n, varying 0 ≤ α ≤ π / 2. In the first case, projections of the surfaces on a diagram C ij × C kl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.

Thermal entanglement in a triple quantum dot system

We present studies of thermal entanglement of a three-spin system in triangular symmetry. Spin correlations are described within an effective Heisenberg Hamiltonian, derived from the Hubbard Hamiltonian, with super-exchange couplings modulated by an effective electric field. Additionally a homogenous magnetic field is applied to completely break the degeneracy of the system. We show that entanglement is generated in the subspace of doublet states with different pairwise spin correlations for the ground and excited states. At low temperatures thermal mixing between the doublets with the same spin destroys entanglement, however one can observe its restoration at higher temperatures due to the mixing of the states with an opposite spin orientation or with quadruplets (unentangled states) always destroys entanglement. Pairwise entanglement is quantified using concurrence for which analytical formulae are derived in various thermal mixing scenarios. The electric field plays a specific role -- it breaks the symmetry of the system and changes spin correlations. Rotating the electric field can create maximally entangled qubit pairs together with a separate spin (monogamy) that survives in a relatively wide temperature range providing robust pairwise entanglement generation at elevated temperatures.

Violation of the “information–disturbance relationship” in finite-time quantum measurements

The effect of measurement attributes (quantum level of precision, finite duration) on the classical and quantum correlations is analyzed for a pair of qubits immersed in a common reservoir. We show that the quantum discord is enhanced as the precision of the measuring instrument is increased, and both the classical correlation and the quantum discord experience noticeable changes during finite-time measurements performed on a neighboring partition of the entangled system. The implication of these results on the “information–disturbance relationship” is examined, with critical analysis of the delicate roles played by quantum non-locality and non-Markovian dynamics in the violation of this relationship, which appears surprisingly for a range of measurement attributes. This work highlights that the fundamental limits of quantum mechanical measurements can be altered by exchanges of non-classical correlations such as the quantum discord with external sources, which has relevance to cryptographic technology.

Centre-of-mass motion-induced decoherence and entanglement generation in a hybrid quantum repeater

Quantum communication over long distances relies on the ability to create entanglement between two remote quantum nodes. Recent proposals aiming at experimental realization propose a hybrid quantum repeater setup where two distant material qubits are entangled by light–matter interaction. Motivated by these developments, we investigate possible decoherence effects originating from the centre-of-mass motion of the spatially well-separated trapped qubits. Within the Lamb–Dicke regime we use photon exchange involving coherent states of the radiation field to entangle the two material qubits. Optimal generalized photonic field measurements are used to achieve entangled qubit pairs with high fidelities and high success probabilities. We demonstrate that the quality of the achievable two-qubit entanglement crucially depends on the trap frequencies involved. Furthermore, dynamical decoupling schemes are proposed which are capable of suppressing centre-of-mass motion-induced decoherence effects significantly and which involve only local operations acting on the spatially well-separated material qubits.

Quantum State Transfer Between Any Pair of Qubits in a Quantum Network via Optical Fibers

We propose scheme for transferring quantum state between any pair of nodes in a quantum network. Each node consists of an atom and a cavity, with the atom acting as the quantum bit. Any two adjacent nodes are connected by an optical fiber. During the operation neither the atomic system nor the fibers are excited, which is important in view of decoherence. Under certain conditions, the probability that the cavities are excited is negligible. The method has an inherent robustness against the fluctuation perturbations in the classical control parameters and the randomness in the atomic position. The scheme can be generalized to implement quantum phase gate between any two remote qubits.

DIAGONAL-UNITARY 2-DESIGN AND THEIR IMPLEMENTATIONS BY QUANTUM CIRCUITS

We study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be achieved by quantum circuits composed of a few-qubit diagonal gates. We introduce diagonal-unitaryt-designs and present two quantum circuits that implement diagonal-unitary 2-design with the computational basis in N-qubit systems. One is composed of single-qubit diagonal gates and controlled-phase gates with randomized phases, which achieves an exact diagonal-unitary 2-design after applying the gates on all pairs of qubits. The number of required gates is N(N - 1)/2. If the controlled-Z gates are used instead of the controlled-phase gates, the circuit cannot achieve an exact 2-design, but achieves an ϵ-approximate 2-design by applying gates on randomly selected pairs of qubits. Due to the random choice of pairs, the circuit obtains extra randomness and the required number of gates is at most O(N2(N + log 1/∊)). We also provide an application of the circuits, a protocol of generating an exact 2-design of random states by combining the circuits with a simple classical procedure requiring O(N) random classical bits.

Correlation Distance and Bounds for Mutual Information

The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information between pairs of two-valued classical variables and quantum qubits, in terms of the corresponding classical and quantum correlation distances. These bounds are stronger than the Pinsker inequality (and refinements thereof) for relative entropy. The classical lower bound may be used to quantify properties of statistical models that violate Bell inequalities. Entangled qubits can have a lower mutual information than can any two-valued classical variables having the same correlation distance. The qubit correlation distance also provides a direct entanglement criterion, related to the spin covariance matrix. Connections of results with classically-correlated quantum states are briefly discussed.

A density functional theory approach to the magnetic properties of a coupled single-molecule magnet (Mn7)2 complex — An entangled qubit pair candidate

The exchange coupling constants of a Mn14 complex constituted by two weakly coupled Mn7 moieties were calculated using two different density functional theory (DFT) approaches: the Perdew–Burke–Ernzerhof (PBE) functional with a numerical basis set and the hybrid Becke, three-parameter Lee–Yang–Parr (B3LYP) functional employed with a Gaussian basis set. The sign and relative strength of the exchange coupling constants calculated with both methods were consistent; as expected, the values calculated with the PBE functional were slightly overestimated, as corroborated by comparison with the experimental magnetic susceptibility curve. Both methods gave a ground spin configuration of S = 3/2 for the Mn7 moiety, which was weakly antiferromagnetically coupled with the other Mn7 fragment, leading to an S = 0 ground spin configuration for the entire Mn14 complex.

Complete tomography of a high-fidelity solid-state entangled spin–photon qubit pair

Entanglement between stationary quantum memories and photonic qubits is crucial for future quantum communication networks. Although high-fidelity spin-photon entanglement was demonstrated in well-isolated atomic and ionic systems, in the solid-state, where massively parallel, scalable networks are most realistically conceivable, entanglement fidelities are typically limited due to intrinsic environmental interactions. Distilling high-fidelity entangled pairs from lower-fidelity precursors can act as a remedy, but the required overhead scales unfavourably with the initial entanglement fidelity. With spin-photon entanglement as a crucial building block for entangling quantum network nodes, obtaining high-fidelity entangled pairs becomes imperative for practical realization of such networks. Here we report the first results of complete state tomography of a solid-state spin-photon-polarization-entangled qubit pair, using a single electron-charged indium arsenide quantum dot. We demonstrate record-high fidelity in the solid-state of well over 90%, and the first (99.9%-confidence) achievement of a fidelity that will unambiguously allow for entanglement distribution in solid-state quantum repeater networks.

Probing the degree of non-Markovianity for independent and common environments

We study the non-Markovianity of the dynamics of open quantum systems, focusing on the cases of independent and common environmental interactions. We investigate the degree of non-Markovianity quantified by two distinct measures proposed by Luo, Fu, and Song and Breuer, Laine, and Pillo. We show that the amount of non-Markovianity, for a single qubit and a pair of qubits, depends on the quantum process, the proposed measure, and whether the environmental interaction is collective or independent. In particular, we demonstrate that while the degree of non-Markovianity generally increases with the number of qubits in the system for independent environments, the same behavior is not always observed for common environments. In the latter case, our analysis suggests that the amount of non-Markovianity could increase or decrease depending on the properties of the considered quantum process.

Quantum simulation architecture for lattice bosons in arbitrary, tunable, external gauge fields

I describe a lattice of asymmetrical qubit pairs in arbitrary dimension, with couplings arranged so that the motion of single-qubit excited states mimics the behavior of charged lattice bosons hopping in a magnetic field. I show, in particular, that one can choose the parameters of the many-body circuit to reach a regime where the complex hopping phase between any two elements can be tuned to any value by simply adjusting the relative phases of two applied oscillating voltage signals. I also propose specific realizations of our model using coupled three junction flux qubits or transmon qubits, in which one can reach the strongly interacting bosonic quantum Hall limit where one will find anyonic excitations. This model could also be studied in trapped ions, and the superconducting circuits could be used for topological quantum computation.

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.

Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations

We address the experimental determination of entropic quantum discord for systems made of a pair of polarization qubits. We compare results from full and partial tomography and found that the two determinations are statistically compatible, with partial tomography leading to a smaller value of discord for depolarized states. Despite the fact that our states are well described, in terms of fidelity, by families of depolarized or phase-damped states, their entropic discord may be largely different from that predicted for these classes of states, such that no reliable estimation procedure beyond tomography may be effectively implemented. Our results, together with the lack of an analytic formula for the entropic discord of a generic two-qubit state, demonstrate that the estimation of quantum discord is an intrinsically noisy procedure. Besides, we question the use of fidelity as a figure of merit to assess quantum correlations.

Probabilistically Controlled Teleportation of an Arbitrary Two-Qubit State via Positive Operator-Valued Measure

We propose a tripartite scheme for probabilistically teleporting an arbitrary two-qubit state with a four-qubit cluster-class state and a Bell-class state as the quantum channels. In the scheme, the sender and the controller make Bell-state measurements (BSMs) on their respective qubit pairs. With their measurement results, the receiver can reconstruct the original state probabilistically by introducing two auxiliary particles and making appropriate unitary operations and positive operator-valued measure (POVM) instead of usual projective measurement. Moreover, the total success probability and classical communication cost of the present protocol are also worked out.

Probabilistic and controlled teleportation of an arbitrary single-qubit state via 1D four-qubit cluster-type state and positive operator-valued measure

A tripartite scheme for probabilistically teleporting an arbitrary single-qubit state with 1D four-qubit cluster-type state as the quantum channel has been proposed. In the scheme, the sender and the controller both perform a Bell-state measurement on their respective qubit pair in their hands and announce the measurement results via classical communication. With the help of the sender and the controller, the receiver can reconstruct the original state with a certain probability by introducing an auxiliary qubit and making appropriate unitary operations and positive operator-valued measures. Moreover, the total success probability and classical communication cost of the present scheme are also calculated.

Quantum-state transfer via resonant tunneling through local-field-induced barriers

Efficient quantum-state transfer is achieved in a uniformly coupled spin-1/2 chain, with open boundaries, by application of local magnetic fields on the second and last-but-one spins, respectively. These effective \textit{barriers} induce appearance of two eigenstates, bi-localized at the edges of the chain, which allow a high quality transfer also at relatively long distances. The same mechanism may be used to send an entire e-bit (e.g., an entangled qubit pair) from one to the other end of the chain.

Analyses of the consistent eavesdropping attack of several eavesdroppers on the ping-pong protocol with entangled pairs of qubits

In this paper the analyses of the eavesdropping attack of two or more eavesdroppers on the original ping-pong protocol with entangled pairs of qubits is carried out. General recursive expression for probability d of attack detection for any number n of eavesdroppers that allows to calculate this probability through the corresponding probability when n – 1 eavesdroppers attack is obtained. It is shown that an increase in the number of attackers in the quantum channel leads to an increase in the probability of detecting these attacks by legitimate users. The expressions for the maximum eavesdroppers' amount of information during a consistent attack of two and three eavesdroppers are obtained. It is indicated that the maximum eavesdroppers' amount of information determined by the same expression as in the case of one eavesdropper's attack, only the value of d is varying. It is shown that the ping-pong protocol with pairs of entangled qubits is vulnerable to eavesdropping attack of several eavesdroppers not more than to one eavesdropper's attack.

SECURITY ENHANCED DIRECT QUANTUM COMMUNICATION WITH HIGHER BIT-RATE

A scheme for deterministic secure direct communication based on ping-pong protocol without restricting the security control only to a distinct control mode and debate via classical channel is proposed. It utilizes an entangled pair of qubits and presents a higher bit-rate transfer of information together with a higher security than ping-pong protocol. The security of protocol is enhanced by introducing a control factor for each message mode. It is explicitly showed that the protocol has a high degree of security against a class of individual attacks, and successfully resolves the famous Wojcik attack.

Kvantova teleportatsiya zashumlenykh zaplutanykh staniv

On the basis of a system of four qubits, the influence of white and colored noises in the states of initially prepared entangled qubit pairs on the final state obtained as a result of the entanglement swapping has been considered. The corresponding density matrices are obtained, and the redistribution of fractions for the pure state and white and colored noises is analyzed. Conditions for the entanglement preservation and destruction in the course of the transition from the initial to the final state are determined. A comparison between the von Neumann entropy for the initial and final states of qubits is carried out.

Exact dynamics of interacting qubits in a thermal environment: results beyond the weak coupling limit

We demonstrate an exact mapping of a class of models of two interacting qubits in thermal reservoirs to two separate problems of spin–boson-type systems. Based on this mapping, exact numerical simulations of the qubits dynamics can be performed, beyond the weak system–bath coupling limit and the Markovian approximation. Given the time evolution of the system population and coherences, we study as an application the dynamics of entanglement between the pair of qubits immersed in boson thermal baths, showing a rich phenomenology, including an intermediate oscillatory behavior, the entanglement sudden birth, sudden death and revival. We find that the occurrence of entanglement sudden death in this model depends on the portion of the zero and double excitation states in the subsystem initial state. In the long-time limit, analytic expressions are presented at weak system–bath coupling, for a range of relevant qubit parameters.