Effect of static disorder in an electron Fabry-Perot interferometer with two quantum scattering centers

Abstract

In a recent paper -F. Ciccarello et al., New J. Phys. 8, 214 (2006) -we have demonstrated that the electron transmission properties of a one-dimensional (1D) wire with two identical embedded spin-1/2 impurities can be significantly affected by entanglement between the spins of the scattering centers. Such effect is of particular interest in the control of transmission of quantum information in nanostructures and can be used as a detection scheme of maximally entangled states of two localized spins. In this letter, we relax the constraint that the two magnetic impurities are equal and investigate how the main results presented in the above paper are affected by a static disorder in the exchange coupling constants of the impurities. Good robustness against deviation from impurity symmetry is found for both the entanglement dependent transmission and the maximally entangled states generation scheme.PACS numbers: 03.67. Mn, 85.35.Ds The key role that entanglement plays in quantum information processing has been investigated over the past few years [1]. In this framework, the role that it plays in quantum transport in mesoscopic systems has been analyzed [2]. Recently, we have shown a novel way in which entanglement can be used for controlling electron transport in nanostructures [3]. Assume to have a 1D wire where two spin-1/2 impurities are embedded at a fixed distance. Such system can be regarded as the electron analogue of a Fabry-Perot (FP) interferometer, with the impurities playing the role of two mirrors with a spin quantum degree of freedom. Single electrons are injected into the wire and undergo multiple scattering between the two magnetic impurities due to the presence of a contact exchange electron-impurity coupling. At each scattering event spin-flip may occur and thus the transmitted spin state of the overall system will be generally different from the incoming one. The typical behaviour shown by electron transmittivity T consists of a loss of electron coherence and thus of a resonance condition T = 1, due to the presence of internal spin degrees of freedom of the scattering centers [4]. Such a system is indeed the electron analogue of a Fabry-Perot (FP) interferometer, with the impurities playing the role of two mirrors with a spin quantum degree of freedom. However, unlike the standard FP device where scattering with each mirror introduces a well-fixed phase shift, in the present system the above phase shifts depend on the electron-impurities spin state and thus, in general, a resonance condition cannot take place. However, the presence of quantum scatterers allows one to investigate if and to what extent maximally entangled states of the impurity spins can affect electron transmission. Denot-ing by |Ψ ± = 2 − 1 2 (|↑↓ ± |↓↑ ) the triplet and singlet maximally entangled spin states of the impurities, respectively, we have thus found that when |Ψ − is prepared, a perfect resonance condition T = 1 can be always reached at electron wave vectors fulfilling kx 0 = nπ (n integer, x 0 the distance between...

Teleportation between distant qudits via scattering of mobile qubits

“…Overall, the protocol therefore exhibits quite a striking resilience against static disorder in the pattern of coupling strengths and a reasonable tolerance against an imperfect matching of resonance conditions (4) and (5). The outcomes of this analysis are in line with similar studies carried out to test the resilience of some scattering-based entanglement generation schemes [13] and provide further evidence of the low level of control required by scattering-based methods to perform QIP tasks.…”

Implementing quantum gates through scattering between a static and a flying qubit

“…Such generally good resilience is in line with the outcomes of analogous tests in similar setups [5,8,9], which further confirms a major advantage of scattering-based methods in accomplishing QIP tasks (see the introduction).…”

“…A well-known major hindrance to the reliable accomplishment of quantum coherent operations stems from the noise that any required manipulation of quantum "hardware" inevitably introduces whenever a given task is to be achieved. Within this framework, an approach that is becoming increasingly popular is to encode the computational space in the (pseudo-) spin degrees of freedom of scattering particles and harness their interaction during the collision to process quantum information [2][3][4][5][6][7][8][9][10][11]. Scattering is indeed a typical phenomenon occurring under low-control conditions: Two or more particles are prepared so as to undergo scattering and eventually measured once this has concluded.…”

“…This makes the accomplishment of QIP tasks, and more in general coherent operations, rather demanding. Indeed, while the works carried out along this line have targeted entanglement generation [2][3][4][5][6][7][8][9] and quantum state tomography [10], only the latest achievements have proved the possibility of performing a quantum algorithm such as teleportation [11]. The working principle behind this recent proposal, however, basically relies on a scatteringbased effective projective measurement of the singlet state of two remote scattering centers [11], that is, the same basic mechanism underpinning previous works that addressed entanglement generation [5][6][7][8].…”

Quasideterministic realization of a universal quantum gate in a single scattering process

“…As a major motivation, this is the only way to jointly address quantum registers located far from each other, thus featuring no direct mutual interaction (this is usually sought to favor local addressing). Within this general framework, over the past few years a research line has thrived around the idea that the crosstalk between the static qubits can be mediated by particles scattering from them [4][5][6][7][8][9][10][11][12][13][14][15].Yet, all of such strategies unavoidably face an inherent major drawback. For a given quantum task to be efficiently accomplished, the link between the static objects should occur by means of the local interaction of each static object with a quantum flying bus.…”