Initial Qubit State Research Articles

Entanglement Between Two Dipole-Coupled Qubits Interacting with Two Independent Slightly Detuned Cavity Modes

Considering the generalized double Jaynes-Cummings model, we examine the entanglement between two non-identical dipole-dipole coupled qubits interacting with two independent detuned vacuum cavity modes. We calculate the negativity as a measure of qubits entanglement. We find that entanglement parameter evolve periodically with time and the period are affected by the model parameters and initial states of qubits. For unentangled initial states the detuning and dipole-dipole interaction affect only the period of entanglement oscillations, not the maximum value of entanglement. For entangled states the detuning stabilizes the entanglement parameter oscillations. According to choice of initial entangled state the dipole-dipole strength is greatly enhances or weakens the oscillations of the entanglement parameter.

Connecting velocity and entanglement in quantum walks

We investigate the relation between transport properties and entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional discrete time quantum walks. We obtain closed-form expressions for the long-time position variance and asymptotic entanglement of quantum walks whose time evolution is given by any balanced quantum coin, starting from any initial qubit and position states following $\delta$-like (local) and Gaussian distributions. We find out that the knowledge of the limit velocity of the walker together with the polar angle of the initial qubit provide the asymptotic entanglement for local states, while this velocity with the quantum coin phases give it for highly delocalized states.

Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball

For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed minimal error probability (i.e., the minimal error distinguishability time). For the case of unitary dynamics generated by a time-independent Hamiltonian, we derive a necessary and sufficient condition on two asymmetry monotones that guarantees that an arbitrary state of a two-level quantum system or a separable state of N two-level quantum systems will unitarily evolve to another state from which it can be distinguished with a fixed minimal error probability δ∈[0,1/2]. This condition is used to order the set of qubit states based on their distinguishability time, and to derive an optimal release time for driven two-level systems such as those that occur, e.g., in the Landau-Zener problem. For the case of non-unitary dynamics, we compare three lower bounds to the distinguishability time, including a new type of lower bound which is formulated in terms of the asymmetry of the uniformly time-twirled initial system-plus-environment state with respect to the generator HSE of the Stinespring isometry corresponding to the dynamics, specifically, in terms of ‖[HSE,ρav(τ)]‖1, where ρav(τ):=1τ∫0τdte−iHSEtρ⊗|0⟩E⟨0|EeiHSEt.

Quantum speed limit for qubit systems: Exact results

Given an initial state, a target state, and a driving Hamiltonian, how fast can the initial state evolve into the target state according to the Schröchinger dynamics? This problem arises in a variety of contexts such as quantum computation, quantum control, and in particular, the problem of maximum information processing rate of quantum systems, and has been studied extensively due to its fundamental importance. In this paper, we purse further the study in the qubit case in which the particular structure admits stronger results. We use the quantum fidelity as well as relative entropy as a figure of merit to characterize the closeness between a fixed initial qubit state and another one undergoing unitary evolution. We work out explicitly maximal and minimal fidelity and relative entropy by determining the closest and the farthest states to the target state and show that these results are unique for qubit systems. We also determine the minimal time for a state to evolve to the extremal states (that is, the farthest one evolved from the initial state in the sense of minimal fidelity or maximal relative entropy), which generalizes the celebrated Mandelstam–Tamm bound and the Margolus–Levitin bound for qubit systems. We further reveal an interesting fact that this minimal time is independent of the initial states.

Analog quantum simulation of the Rabi model in the ultra-strong coupling regime

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes–Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.

Estimation of two-qubit interactions through channels with environment assistance

We consider the estimation of two-qubit interactions when initial states of both qubit can be locally controlled, while the final state of only one qubit can be measured. This amounts to realize a model of quantum channel communication with environment assistance. In such a framework, the unitaries’ parameters space results a tetrahedron in [Formula: see text]. On its edges the problem, becoming of single parameter estimation, can be exactly solved and we derive optimal probe states and estimators. Our results show that the possibility of environment assistance is always beneficial, while the usage of entanglement at channels’ input is not.

Qubit–qubit entanglement dynamics control via external classical pumping and Kerr nonlinearity mediated by a single detuned cavity field powered by two-photon processes

The nonlinear time-dependent two-photon Hamiltonian of a couple of classically pumped independent qubits is analytically solved, and the corresponding time evolution unitary operator, in an exact form, is derived. Using the concurrence, entanglement dynamics between the qubits under the influence of a wide range of effective parameters are examined and, in detail, analyzed. Observations analysis is documented with aid of the field phase-space distribution Wigner function. A couple of initial qubit states is considered, namely similar excited states and a Bell-like pure state. It is demonstrated that an initial Bell-like pure state is as well typical initial qubits setting for robust, regular and a high degree of entanglement. Moreover, it is established that high-constant Kerr media represent an effective tool for generating periodical entanglement at fixed time cycles of maxima reach unity forever when qubits are initially in a Bell-like pure state. Further, it is showed that the medium strength of the classical pumping stimulates efficiently qubits entanglement, specially, when the interaction occurs off resonantly. However, the high-intensity pumping thermalizes the coherent distribution of photons, thus, the least photons number is used and, hence, the least minimum degree of qubits entanglement could be created. Furthermore, when the cavity field and external pumping are detuned, the external pumping acts like an auxiliary effective frequency for the cavity, as a result, the field Gaussian distribution acquires linear chirps, and consequently, more entanglement revivals appear in the same cycle during timescale.

Generation of chiral spin state by quantum simulation

Chirality of materials in nature appears when there are asymmetries in their lattice structures or interactions in a certain environment. Recent development of quantum simulation technology has enabled the manipulation of qubits. Accordingly, chirality can be realized intentionally rather than passively observed. Here we theoretically provide simple methods to create a chiral spin state in a spin-1/2 qubit system on a square lattice. First, we show that switching ON/OFF the Heisenberg and $XY$ interactions produces the chiral interaction directly in the effective Hamiltonian without controlling local fields. Moreover, when initial states of spin-qubits are appropriately prepared, we prove that the chirality with desirable phase is dynamically obtained. Finally, even for the case where switching ON/OFF the interactions is infeasible and the interactions are always-on, we show that, by preparing an asymmetric initial qubit state, the chirality whose phase is $\pi/2$ is dynamically generated.

Preparation and non-classical characteristics of two-mode entangled coherent state

We propose a scheme to generate two-mode entangled coherent states using a Λ-type rf-SQUID qubit to induce the interaction between two transmission line resonators (TLRs). The proposed scheme takes advantage of the easy integration of solid quantum circuit. Through investigating the dynamical evolution, we find the relationship between the initial quantum state of the superconducting qubit and the quantum entanglement of the field modes. We analyze as well the influence of decoherence effect on the non-classical characteristics of the optical field by means of the density operator, fidelity and Mandel Q. The investigation results indicate that one should first optimize the preparation of the initial quantum state of qubit so as to prepare two-mode entangled state with high entanglement degree and obvious non-classical characteristics. The qubit initially prepared in (|0〉+|1〉)/2 does not get entangled with the two modes of field. Inversely, the qubit can effectively improve the degree of entanglement between field modes and obviously promote the anti-bunching effect and squeezing effect if it is initially prepared in ground state |0〉.

Distributed manipulation of two-qubit entanglement with coupled continuous variables

We study the dynamics of two qubits separately sent through two coupled resonators, each initially containing a coherent-state field. We present analytical arguments and numerically approximate solutions for the qubit-field system under different two-qubit initial states, photon-hopping strengths, and detunings. In the far off-resonant regime, the maximal entanglement of two qubits can be generated with the initial qubit state in which one qubit is in the excited state and the other is in the ground state, and the initially maximal two-qubit entanglement can be frozen and fully revived even for large mean photon number. When the qubits are both initially in their excited states or ground states, qubit–qubit entanglement birth and death apparently appear in the regime where the photon-hopping strength is close to qubit-field detuning, and its peaks do not decrease monotonically as the interaction time increases. It is interesting to observe that when there is photon hopping between two fields, the field–field entanglement can be larger than 1 and increases as the initial amplitude of the coherent state grows. Our present setup is fundamental for distributed quantum information processing and applicable to different physical qubit-resonator systems.

Controlling sudden transitions of bipartite quantum correlations under dephasing via dynamical decoupling

Sudden transitions of one-norm geometric quantum discord and quantum discord of quantum systems have been observed in experiments recently. We propose a scheme to control sudden transitions of quantum correlations of two qubits within two spatially separated thermal baths or one common thermal bath via bang-bang pulses with a finite period. For the two-bath case, correlations decrease with time, and the sudden transition behavior can be efficiently adjusted by bang-bang pulses. For one common bath case, the thermal bath may play a constructive or destructive role in the generation of steady-state correlations, depending on the initial state of qubits.

Optimal signal processing for continuous qubit readout

The measurement of a quantum two-level system, or a qubit in modern terminology, often involves an electromagnetic field that interacts with the qubit, before the field is measured continuously and the qubit state is inferred from the noisy field measurement. During the measurement, the qubit may undergo spontaneous transitions, further obscuring the initial qubit state from the observer. Taking advantage of some well known techniques in stochastic detection theory, here we propose a novel signal processing protocol that can infer the initial qubit state optimally from the measurement in the presence of noise and qubit dynamics. Assuming continuous quantum-nondemolition measurements with Gaussian or Poissonian noise and a classical Markov model for the qubit, we derive analytic solutions to the protocol in some special cases of interest using It\={o} calculus. Our method is applicable to multi-hypothesis testing for robust qubit readout and relevant to experiments on qubits in superconducting microwave circuits, trapped ions, nitrogen-vacancy centers in diamond, semiconductor quantum dots, or phosphorus donors in silicon.

Experimental simulation of closed timelike curves.

Closed timelike curves are among the most controversial features of modern physics. As legitimate solutions to Einstein's field equations, they allow for time travel, which instinctively seems paradoxical. However, in the quantum regime these paradoxes can be resolved, leaving closed timelike curves consistent with relativity. The study of these systems therefore provides valuable insight into nonlinearities and the emergence of causal structures in quantum mechanics--essential for any formulation of a quantum theory of gravity. Here we experimentally simulate the nonlinear behaviour of a qubit interacting unitarily with an older version of itself, addressing some of the fascinating effects that arise in systems traversing a closed timelike curve. These include perfect discrimination of non-orthogonal states and, most intriguingly, the ability to distinguish nominally equivalent ways of preparing pure quantum states. Finally, we examine the dependence of these effects on the initial qubit state, the form of the unitary interaction and the influence of decoherence.

Quantum Chernoff bound as a measure of the efficiency of quantum cloning for mixed states

In this paper we investigate the efficiency of quantum cloning of N identical mixed qubits. We employ a recently introduced measure of distinguishability of quantum states called the quantum Chernoff bound. We evaluate the quantum Chernoff bound between the output clones generated by the cloning machine and the initial mixed qubit state. Our analysis is illustrated by performing numerical calculation of the quantum Chernoff bound for different scenarios that involves the number of initial qubits N and the number of output imperfect copies M.

Geometric Measure of Nonlocality and Quantum Discord of Two Charge Qubits with Phase Decoherence and Dipole-Dipole Interaction

The effects of both phase decoherence and dipole-dipole interaction on quantum correlations of superconducting (SC) charge qubits, placed in a single-mode SC-cavity, are investigated. When the initial qubit-states are unentangled, measurement-induced nonlocality (MIN), geometric quantum discord (GQD) and quantum entanglement (QE) have different evolutions. They remain at stationary nonzero values with phase decoherence. These stationary correlations clearly appear with the photon number of Fock state. The quantum correlations can be enhanced by dipole-dipole interaction that can weaken the phase decoherence effect. When the initial states of charge qubits are entangled, the appearance of the stationary correlations can be accelerated by the photon number. The correlations can be also increased by the dipole-dipole interaction. These increases can be weaken by the photon number. The photon number also leads to sudden death and sudden birth for QE while MIN periodically reaches its maximum values, but GQD decays continuously with respect to time until it tends to be zero. When the states of the qubits have no entanglement nor entanglement sudden death, MIN and GQD keep nonzero values. The steady-state of correlations is calculated. It is found that these correlations depend on the initial states, the photon number and the dipole-dipole interaction.

Initial states of qubit–environment models leading to conserved quantities

It is possible to prepare a composite qubit–environment system so that its time evolution will guarantee the conservation of a preselected qubit’s observable. In general, this observable is not associated with a symmetry. The latter may not even be present in the subsystem. The initial states which lead to such a quantity conserved dynamics form a subspace of the qubit–environment space of states. General construction of this subspace is presented and illustrated by two examples. The first one is the exactly solvable Jaynes–Cummings model and the second is the multi-photon Rabi model.

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.

Tensor-product representation of qubits and tensor realization of one-qubit operators

We consider one-particle spin states. We show that all the information contained in the state can be written in an equivalent form using three completely decohered mixed states. The density matrix of such a system has the form of tensor product of three diagonal matrices. The unitary operators defined in the space of one-particle spin states are represented by some transformation of tensor products of diagonal matrices. We determine the explicit form of the unitary transformations acting on the representing three-qubit system and corresponding basic operators acting in the space of the initial qubit states.

The dynamics of quantum discord and entanglement of two atoms coupled to two spatially separate cavities in cavity QED

In this paper, we study the dynamics of quantum discord and entanglement of two identical two-level atoms A and B coupled with two spatially separate single-mode high-Q cavities a and b in cavity QED, respectively. Making use of geometrical depiction of quantum discord and entanglement of formation (EoF), we show that there exists quantum discord sudden death (DSD) as well as entanglement sudden death (ESD) and the time interval of DSD is shorter than that of ESD in the presented quantum system. In addition, the rate of decreasing of quantum discord is slower than that of entanglement. We have shown that the amount of quantum discord and entanglement and the relative ordering between quantum discord and quantum entanglement depend on the purity p in the presented quantum system. And we have also shown that quantum discord and entanglement of the qubits AB can transfer to the cavities ab and vice versa. Moreover, the transfer of quantum discord is independent of the purity p but that of quantum entanglement is dependent of the purity p. Surprisingly, the sudden changes of quantum discord of qubits and cavities are observed when the initial states of qubits are mixed.

Interplay of Quantum Stochastic and Dynamical Maps to Discern Markovian and Non-Markovian Transitions

It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1, t2 (t2 > t1), are both completely positive (CP) but in the intermediate times between t1 and t2 it need not be CP. This reveals the key to the Markov (if CP) and non Markov (if it is not CP) avataras of the intermediate dynamics. This is brought out here in terms of the quantum stochastic map A and the associated dynamical map B—without resorting to master equation approaches. We investigate these features with four examples which have entirely different physical origins: 1) A two qubit Werner state map with time dependent noise parameter; 2) Phenomenological model of a recent optical experiment (Nature Physics, 7, 931 (2011)) on the open system evolution of photon polarization; 3) Hamiltonian dynamics of a qubit coupled to a bath of N qubits; 4) Two qubit unitary dynamics of Jordan et al. (Phys. Rev. A 70, 052110 (2004) with initial product states of qubits. In all these models, it is shown that the positivity/negativity of the eigenvalues of intermediate time dynamical B map determines the Markov/non-Markov nature of the dynamics.