Perfect state transfer is possible in modulated spin chains, imperfections however are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.
In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the well-known one dimensional cases, such as 1d spin chains. We use methods from fractal analysis and probability to find a new class of quantum spin chains on fractal-like graphs (known as diamond fractals) which support perfect quantum state transfer, and which have a wide range of different Hausdorff and spectral dimensions. The resulting systems are spin networks combining Dyson hierarchical model structure with trans…
In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer: the transmission of quantum states without dissipation. The essential goal is to develop the theoretical framework for understanding the interplay between perfect quantum state transfer, spectral properties, and the geometry of the underlying graph, in order to design novel protocols for applications in quantum information science. We present a new lifting and gluing construction, and use this to prove results concerning an inductive spectr…
A recent scheme for perfect transmission of quantum states through quasi-one dimensional chains requires application of global control at regular intervals of time. We study the effect of stochastic noise in this control and find that the scheme is robust for reasonable values of disorder. Both un-correlated and correlated noise in the external control are studied and it is remarkably found that the efficiency of the protocol is much higher in presence of correlated noise.
A method for realizing asymmetric (one-way) transmission of discretized light in modulated, linear and purely passive optical lattices is suggested, which exploits the idea of unidirectional coherent perfect absorption. The system consists of a linear photonic lattice of coupled resonators or waveguides, side coupled to a chain of lossy elements, in which light can avoid the occupation of the dissipative sites when propagating in one way, but not in the opposite one. Non-reciprocity requires modulation of the resonator/waveguide parameters, realizing a dissipative optical Aharonov-Bohm diode w…
We show how to efficiently send an M-partite entangled state along a spin chain of arbitrary size. Specifically, we show how an entangled M-partite W sate can be almost flawlessly transmitted from one end (Alice) to the other end (Bob) of a spin-1/2 chain described by a slightly modified XX model. We achieve an almost perfect transmission without employing external magnetic fields or modulating the coupling constants among the spins of the chain, the two standard approaches used to achieve a good transmission efficiency. Moreover, the protocol here proposed can be used to transform an M-partit…
We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian quantum mechanical framework from the physical viewpoint. One of the most interesting features of the analysis is that the complex eigenvalues of the underlying non-Hermitian problem, associated with a reflectionless scattering system, lead to the loss of perfect-transmission energies as the parameters characterizing the scattering potential are varied. On the…
We study the protocol known as quantum state transfer for a strongly coupled antiferromagnetic spin chain or ring (acting as a spin bus), with weakly coupled external qubits. By treating the weak coupling as a perturbation, we find that perfect state transfer (PST) is possible when second order terms are included in the expansion. We also show that PST is robust against variations in the couplings along the spin bus and between the bus and the qubits. As evidence of the quantum interference which mediates PST, we show that the optimal time for PST can be smaller with larger qubit separations, …
Nonreciprocal devices are indispensable for building quantum networks and ubiquitous in modern communication technology. Here, we use optomechanical interaction and linearly-coupled interaction to realize optical nonreciprocal transmission in a double-cavity optomechanical system. The scheme relies on the interference between the two interactions. We derive the essential conditions to realize perfect optical nonreciprocity in the system, and analyse the properties of optical nonreciprocal transmission and the output fields from mechanical mode. These results can be used to control optical tran…
We propose a new scheme in which perfect transmission of 1-qubit information is achieved with high success using purposefully delayed sharing of non-maximally entangled 2-qubit resource and repeated generalized Bell-state measurements (GBSM). Alice possesses initially all qubits and she makes repeated GBSM on the pair of qubits, consisting of (1) the qubit of information state and (2) one of the two entangled resource qubits (taken alternately) until transmission with perfect fidelity is indicated. Alice then sends to Bob, the qubit not used in the last GBSM and also the result of this GBSM an…
We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Y-junctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we find compact formulas for probability amplitudes in the ring systems. We also discuss quantum reflection and transmission in the ring systems under scale-invariant junction conditions. It is remarkable that perfect reflection can occur in an anti-symmetric ring system, in contrast with the one-dimensional quantum systems having singular nodes of degree 2.
We propose a scheme for using a spin chain with fixed symmetry interaction as a channel for perfect quantum communication. The perfect quantum communication is determined by the eigenvalues that form a special arithmetical progression, the concrete interaction parameter $J_i$ is obtained as a function of integer and perfect transmission time $t_p$. There are infinite choices of $J_i$ for perfect transmission and one can design the channel according to the requirement of $t_p$. This scheme will provide more choices of spin chain for future experiment in quantum communication.
Suppose that $m$ senders want to transmit classical information to $n$ receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each $m$ and $n$ with $m\ge 2$ or $n\ge 2$, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and i…
The resonant transmission of a moving particle which interacts with an one-dimensional array of N delta-function potentials is investigated. A suitable transfer matrix formulation is used to obtain the particle transmission. We give the parameters for perfect tunnelling and the transcendental equation for the quasi-bound state energies for N = 2, 3 and 4. Conditions for perfect tunnelling and resonant transmission are discussed for arrays with arbitrary N. A model to explain how the tunnelling energy filter works in these systems is proposed here.
We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed.
An essential attribute of many fractal structures is self-similarity. A Sierpinski gasket (SPG) triangle is a promising example of a fractal lattice that exhibits localized energy eigenstates. In the present work, for the first time we establish that a mixture of both extended and localized energy eigenstates can be generated yeilding mobility edges at multiple energies in presence of a time-periodic driving field. We obtain several compelling features by studying the transmission and energy eigenvalue spectra. As a possible application of our new findings, different thermoelectric properties …
We study a general double Dirac delta potential to show that this is the simplest yet versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission ($T=1$). Perfect transmission energies turn out to be the critical property of symmetric and anti-symmetric cases wherein these discrete energies are found to correspond to the eigenvalues of Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission [or zero reflectivity, $R(E)$] at energy $E=0$ is non-intuitive. However, earlier this has been…
We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by $U(2)\times U(2)$, which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission occurs. We also provide the physical interpretation of the resonance condition.
We investigate interference and correlation effects when several detuned emitters are placed along a one-dimensional photonic waveguide. Such a setup allows multiple interactions between the photons and the strongly coupled emitters, and underlies proposed devices for quantum information processing. We show, first, that a pair of detuned two-level systems (2LS) separated by a half wavelength mimic a driven Λ-type three-level system (3LS) in both the single- and two- photon sectors. There is an interference-induced transparency peak at which the fluorescence is quenched, leaving the transmitted…
A uniformly coupled double quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission for an arbitrary Hamiltonian including this one. By calculating the eigenvalues and eigenvectors of a unitary operator obtained from the free evolution plus an exchange operator, we find that the double quantum Hamiltonian spin chain will support a three-spin initial encoding that will transfer along the chain with remarkably high fidelity. The fidelity is al…
We consider an exact state transmission, where a density matrix in one information processor A at time $t=0$ is exactly equal to that in another processor B at a later time. We demonstrate that there always exists a complete set of orthogonal states, which can be employed to perform the exact state transmission. Our result is very general in the sense that it holds for arbitrary media between the two processors and for any time interval. We illustrate our results in terms of models of spin, fermionic and bosonic chains. This complete set can be used as bases to study the perfect state transfer…
We propose a procedure for transferring the state a microwave qubit via a transmission line from one resonator to another resonator, with a theoretical efficiency arbitrarily close to 100%. The emission and capture of the microwave energy is performed using tunable couplers, whose transmission coefficients vary in time. Using the superconducting phase qubit technology and tunable couplers with maximum coupling of 100 MHz, the procedure with theoretical efficiency $η=0.999$ requires a duration of about 400 ns (excluding propagation time) and an ON/OFF ratio of 45. The procedure may also be used…
Linear theory for phonon scattering by discrete breathers in the discrete nonlinear Schroedinger equation using the transfer matrix approach is presented. Transmission and reflection coefficients are obtained as a function of the wave vector of the input phonon. The occurrence of a nonzero transmission, which in fact becomes perfect for a symmetric breather, is shown to be connected with localized eigenmodes thresholds. In the weak-coupling limit, perfect reflection are shown to exist, which requires two scattering channels. A necessary condition for a system to have a perfect reflection is al…
