Showing papers in "Physical Review A in 2012"
TL;DR: The concept of the stabilizer, using two qubits, is introduced, and the single-qubit Hadamard, S and T operators are described, completing the set of required gates for a universal quantum computer.
Abstract: This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-not. We then describe the single-qubit Hadamard, Ŝ and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of Appendices in which we provide supplementary information to the main text. © 2012 American Physical Society.
2,205 citations
TL;DR: It is shown that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities and clarifies the link between the security of this one-sided DI- QKD scenario and the demonstration of quantum steering, in analogy to the links between DI-ZKD and the violation of Bell inequalities.
Abstract: We analyze the security and feasibility of a protocol for quantum key distribution (QKD) in a context where only one of the two parties trusts his measurement apparatus. This scenario lies naturally between standard QKD, where both parties trust their measurement apparatuses, and device-independent QKD (DI-QKD), where neither do, and can be a natural assumption in some practical situations. We show that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities. We clarify the link between the security of this one-sided DI-QKD scenario and the demonstration of quantum steering, in analogy to the link between DI-QKD and the violation of Bell inequalities.
610 citations
TL;DR: Bounds on F imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry, and these criteria detect different sets of states and illustrate their strengths by considering several examples.
Abstract: The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $\overline{F}$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $\overline{F}$ is able to detect certain bound entangled states.
421 citations
TL;DR: This work describes and expands upon the scalable randomized benchmarking protocol proposed in Phys.
Abstract: We describe and expand upon the scalable randomized benchmarking protocol proposed in Phys. Rev. Lett. 106, 180504 (2011) which provides a method for benchmarking quantum gates and estimating the gate dependence of the noise. The protocol allows the noise to have weak time and gate dependence, and we provide a sufficient condition for the applicability of the protocol in terms of the average variation of the noise. We discuss how state-preparation and measurement errors are taken into account and provide a complete proof of the scalability of the protocol. We establish a connection in special cases between the error rate provided by this protocol and the error strength measured using the diamond norm distance.
406 citations
TL;DR: In this article, the authors present several entanglement criteria in terms of the quantum Fisher information that help to relate various forms of multipartite entenglement to the sensitivity of phase estimation.
Abstract: We present several entanglement criteria in terms of the quantum Fisher information that help to relate various forms of multipartite entanglement to the sensitivity of phase estimation. We show that genuine multipartite entanglement is necessary to reach the maximum sensitivity in some very general metrological tasks using a two-arm linear interferometer. We also show that it is needed to reach the maximum average sensitivity in a certain combination of such metrological tasks.
385 citations
TL;DR: In this article, the optical properties of one-dimensional symmetric structures of arbitrary complexity were analyzed and generalized unitarity relations were shown to lead to a conservation relation in terms of the transmittance and (left and right) reflectances.
Abstract: We analyze the optical properties of one-dimensional $\mathcal{PT}$-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in $\mathcal{PT}$-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at $\mathcal{PT}$-symmetry-breaking points. The general conservation relations can be utilized as an experimental signature of the presence of $\mathcal{PT}$ symmetry and of $\mathcal{PT}$-symmetry-breaking transitions. The uniqueness of $\mathcal{PT}$-symmetry-breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.
360 citations
TL;DR: In this article, it was shown that the evanescent electromagnetic waves forming the surface polariton inevitably possess a backward spin energy flow, which together with a superluminal orbital energy flow form the total Poynting vector.
Abstract: We consider a $p$-polarized surface electromagnetic wave (a classical surface polariton) at the interface between the vacuum and a metal or left-handed medium. We show that the evanescent electromagnetic waves forming the surface polariton inevitably possess a backward spin energy flow, which, together with a superluminal orbital energy flow, form the total Poynting vector. This spin energy flow generates a well-defined (but not quantized) spin angular momentum of surface polaritons which is orthogonal to the propagation direction. The spin of evanescent waves arises from the imaginary longitudinal component of the electric field which makes the polarization effectively elliptical in the propagation plane. We also examine the connection between the spin and chirality of evanescent modes.
324 citations
TL;DR: In this article, a species-selective dipole potential was used to create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion.
Abstract: Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities' size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach.
300 citations
TL;DR: In this paper, an analog of electromagnetically induced transparency (EIT) in plasmonic systems consisting of multiple cascaded nanodisk resonators, coupled to metal-insulator-metal bus waveguides, was theoretically and numerically investigated.
Abstract: We have theoretically and numerically investigated an analog of electromagnetically induced transparency (EIT) in plasmonic systems consisting of multiple cascaded nanodisk resonators, aperture-side-coupled to metal-insulator-metal bus waveguides. A simplified theoretical model is established to study spectral features in the plasmonic waveguide-resonator systems, and the calculated results are in good agreement with finite-difference time-domain simulations. The main dependent factors of EIT-like spectral response, namely, the resonance detuning, intrinsic Drude loss, and especially cavity-cavity separation, are discussed in detail. Similar to multiple EIT in quantum systems, multiple induced-transparency peaks are found in the areas of strong dispersion generated in our plasmonic system. The group indices and quality factors of transparency resonances with high transmission can reach levels of similar to 35 and similar to 200, respectively. These results pave a way toward dynamic control of light in the nanoscale domain, which can actualize some new devices for fundamental study and applications of plasmonic nanostructures.
296 citations
TL;DR: In this paper, the authors proposed a measure for non-Markovianity by using correlations as quantified by the quantum mutual information rather than entanglement, and a simplified version based on Jamio\l{}kowski-Choi isomorphism which encodes operations via bipartite states and does not involve any optimization.
Abstract: In the study of open quantum systems, memory effects are usually ignored, and this leads to dynamical semigroups and Markovian dynamics. However, in practice, non-Markovian dynamics is the rule rather than the exception. With the recent emergence of quantum information theory, there is a flurry of investigations of non-Markovian dynamics, and several significant measures for non-Markovianity are introduced from various perspectives such as deviation from divisibility, information exchange between a system and its environment, or entanglement with the environment. In this work, by exploiting the correlations flow between a system and an arbitrary ancillary, we propose a considerably intuitive measure for non-Markovianity by use of correlations as quantified by the quantum mutual information rather than entanglement. The fundamental properties, physical significance, and differences and relations with existing measures for non-Markovianity are elucidated. The measure captures quite directly and deeply the characteristics of non-Markovianity from the perspective of information. A simplified version based on Jamio\l{}kowski-Choi isomorphism which encodes operations via bipartite states and does not involve any optimization is also proposed.
290 citations
TL;DR: In this article, the stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one-and two-dimensional systems.
Abstract: Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase transition point), an infinite number of linear Bloch bands turn complex simultaneously Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear Third, we investigate the nonlinear evolution of unstable PT solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the PT lattice is below the phase transition point
Abstract: We argue that the geometric discord introduced by Daki\ifmmode \acute{c}\else \'{c}\fi{}, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)] is not a good measure for the quantumness of correlations, as it can increase even under trivial local reversible operations of the party whose classicality or nonclassicality is not tested. On the other hand it is known that the standard, mutual-information-based discord does not suffer this problem; a simplified proof of such a fact is given.
TL;DR: In this article, the authors investigate dissipative phase transitions in an open central spin system and develop analytical tools based on a self-consistent Holstein-Primakoff approximation that enable them to determine the complete phase diagram associated with the steady states of this system.
Abstract: We investigate dissipative phase transitions in an open central spin system. In our model the central spin interacts coherently with the surrounding many-particle spin environment and is subject to coherent driving and dissipation. We develop analytical tools based on a self-consistent Holstein-Primakoff approximation that enable us to determine the complete phase diagram associated with the steady states of this system. It includes first- and second-order phase transitions, as well as regions of bistability, spin squeezing, and altered spin-pumping dynamics. Prospects of observing these phenomena in systems such as electron spins in quantum dots or nitrogen-vacancy centers coupled to lattice nuclear spins are briefly discussed.
TL;DR: In this article, the authors present an effective operator formalism for open quantum systems, employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, which reduces the evolution to the ground state dynamics.
Abstract: We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method with the hitherto existing concepts for effective interactions and present physical examples for the application of our formalism, including dissipative state preparation by engineered decay processes.
TL;DR: In this paper, the authors proposed two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons, which are implemented with linear optics and with cross-Kerr-nonlinearities.
Abstract: We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon with a certain probability, while the conventional ECPs require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second protocol is implemented with cross-Kerr-nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiments. With cross-Kerr-nonlinearities, it does not require sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it may be the most economical protocol by far. Meanwhile, both protocols are more suitable for multiphoton system concentration because they need less operations and classical communications. All these advantages make the two protocols useful in current long-distance quantum communications.
TL;DR: It is proved that two no-signalling channels that are not perfectly distinguishable in any ordinary quantum circuit can become perfectly distinguishability through the quantum superposition of circuits with different causal structures.
Abstract: A no-signalling channel transforming quantum systems in Alice's and Bob's local laboratories is compatible with two different causal structures: ($A⪯B$) Alice's output causally precedes Bob's input and ($B⪯A$) Bob's output causally precedes Alice's input. Here I prove that two no-signalling channels that are not perfectly distinguishable in any ordinary quantum circuit can become perfectly distinguishable through the quantum superposition of circuits with different causal structures.
TL;DR: In this article, the optical properties of multilayered hyperbolic metamaterials (HMMs) in terms of the Fresnel reflection coefficients at the boundary between the METAMaterial and the ambient medium were analyzed.
Abstract: We express the optical properties of multilayered hyperbolic metamaterials (HMMs) in terms of the Fresnel reflection coefficients at the boundary between the metamaterial and the ambient medium. Formation of a band of bulk propagating modes in HMMs located far outside the lightcone of homogeneous isotropic media is demonstrated. Exotic behavior of HMMs, such as the broadband Purcell effect and suppressed outward scattering, is reproduced. Conditions under which a metal-dielectric multilayer can be approximated by a homogeneous effective medium with extreme anisotropy (indefinite medium) are derived. It is shown that real multilayer HMMs usually have a smaller Purcell factor than the corresponding effective medium; however, the reverse scenario is shown to be possible due to an intermediary role of short-range surface plasmon excitations in the outermost metal layer in a metal-dielectric multilayer.
TL;DR: In this article, the spin Hall effect of light (SHEL) on a nanometal film and demonstrate it experimentally via weak measurements was investigated. And the spin-orbit coupling in the SHEL can be effectively modulated by adjusting the thickness of the metal film, and the transverse displacement is sensitive to thickness of metal film in a certain range for horizontal polarization light.
Abstract: We theorize the spin Hall effect of light (SHEL) on a nanometal film and demonstrate it experimentally via weak measurements. A general propagation model to describe the relationship between the spin-orbit coupling and the thickness of the metal film is established. It is revealed that the spin-orbit coupling in the SHEL can be effectively modulated by adjusting the thickness of the metal film, and the transverse displacement is sensitive to the thickness of metal film in a certain range for horizontal polarization light. Importantly, a large negative transverse shift can be observed as a consequence of the combined contribution of the ratio and the phase difference of Fresnel coefficients.
TL;DR: In this paper, Braak et al. showed that the two-photon Rabi model can be solved exactly by treating extended squeezed states on an equal footing, and the isolated Juddian solutions are also analytically obtained in terms of degeneracy.
Abstract: Within extended coherent states, a recent exact solution to the quantum Rabi model (QRM) [D. Braak, Phys. Rev. Lett. 107, 100401 (2011)] can be recovered in an alternative simpler and more physical way, without use of any extra conditions. In the same framework, the two-photon QRM is solved exactly by treating extended squeezed states on an equal footing. Concise transcendental functions responsible for the exact solutions are derived. The isolated Juddian solutions are also analytically obtained in terms of degeneracy. Both the extended coherent states and squeezed states employed here are essentially Fock states in the space of the corresponding Bogoliubov operators, which result in free-particle number operators. The present approach can be summarized concisely in a unified way and easily extended to various spin-boson systems with multiple levels, even multiple modes.
TL;DR: A new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation on all logical qubits are proposed and lead to a two-fold overhead reduction for distilling magic states with output accuracy compared with the best previously known protocol.
Abstract: We propose a family of error-detecting stabilizer codes with an encoding rate of $1/3$ that permit a transversal implementation of the gate $T=\mathrm{exp}(\ensuremath{-}i\ensuremath{\pi}Z/8)$ on all logical qubits. These codes are used to construct protocols for distilling high-quality ``magic'' states $T\left|+\right\ensuremath{\rangle}$ by Clifford group gates and Pauli measurements. The distillation overhead scales as $O({\mathrm{log}}^{\ensuremath{\gamma}}(1/\ensuremath{\epsilon}))$, where $\ensuremath{\epsilon}$ is the output accuracy and $\ensuremath{\gamma}={\mathrm{log}}_{2}(3)\ensuremath{\approx}1.6$. To construct the desired family of codes, we introduce the notion of a triorthogonal matrix, a binary matrix in which any pair and any triple of rows have even overlap. Any triorthogonal matrix gives rise to a stabilizer code with a transversal $T$ gate on all logical qubits, possibly augmented by Clifford gates. A powerful numerical method for generating triorthogonal matrices is proposed. Our techniques lead to a twofold overhead reduction for distilling magic states with accuracy $\ensuremath{\epsilon}\ensuremath{\sim}{10}^{\ensuremath{-}12}$ compared with previously known protocols.
TL;DR: In this article, the authors investigated correlations among complementary observables and showed how to take advantage of mutually unbiased bases for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite and continuous-variable quantum systems.
Abstract: We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite, and continuous-variable quantum systems. The introduced entanglement criteria are relatively easy to implement experimentally since they require only a few local measurement settings. In addition, we establish a link between the separability problem and the maximum number of mutually unbiased bases---opening an additional avenue in this long-standing open problem.
TL;DR: In this paper, an invariant-based inverse engineering, resonant laser pulses are designed to perform fast population transfers in three-level systems. But the laser intensities to improve the fidelity or to achieve a perfect transfer are examined for different protocols.
Abstract: We design, by invariant-based inverse engineering, resonant laser pulses to perform fast population transfers in three-level systems. The laser intensities to improve the fidelity or to achieve a perfect transfer are examined for different protocols. They can be reduced by populating the intermediate state and by multimode driving.
TL;DR: In this article, the stability properties of the high and low-frequency solitons were determined by a single combination of the soliton's amplitude and the gain-loss coefficient of the waveguides.
Abstract: We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain-loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space, thereby blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.
TL;DR: In this paper, the amplitude of the second-order sideband can be controlled by the strong control field and the weak probe field, respectively, and it is shown that the amplitude can vary with the control field.
Abstract: Higher-order sidebands in optomechanically induced transparency are discussed in a generic optomechanical system. We take account of nonlinear terms and give an effective method to deal with such problems. It is shown that, if a strong control field with frequency ${\ensuremath{\omega}}_{1}$ and a weak probe field with frequency ${\ensuremath{\omega}}_{p}$ are incident upon the optomechanical system, then there are output fields with frequencies ${\ensuremath{\omega}}_{1}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega}$ generated, where $\ensuremath{\Omega}={\ensuremath{\omega}}_{p}\ensuremath{-}{\ensuremath{\omega}}_{1}$. We analyze the amplitude of the output field ${\ensuremath{\omega}}_{1}+2\ensuremath{\Omega}$ and look at how it varies with the control field and show that the amplitude of the second-order sideband can be controlled by the strong control field.
TL;DR: In this article, the authors proposed two two-step entanglement concentration protocols for concentrating an arbitrary three-particle less-entangled state into a maximally entangled $W$ state assisted with single photons.
Abstract: We present two two-step practical entanglement concentration protocols for concentrating an arbitrary three-particle less-entangled $W$ state into a maximally entangled $W$ state assisted with single photons. The first protocol uses the linear optics and the second protocol adopts the cross--Kerr nonlinearity to perform the protocol. In the first protocol, based on the postselection principle, three parties say Alice, Bob, and Charlie in different distant locations can obtain the maximally entangled $W$ state from the arbitrary less-entangled $W$ state with a certain success probability. In the second protocol, the parties are not required to possess the sophisticated single-photon detectors and the concentrated photon pair can be retained after performing this protocol successfully. Moreover, the second protocol can be repeated to get a higher success probability. Both protocols may be useful in practical quantum-information applications.
TL;DR: In this article, the effects of the nonlinearity in the Gross-Pitaevskii equation on the properties of a Bose-Einstein condensate in a double-well potential were investigated.
Abstract: The observation of $\mathcal{PT}$ symmetry in a coupled optical waveguide system that involves a complex refractive index has been demonstrated impressively in the experiment by R\"uter et al. [Nat. Phys. 6, 192 (2010)]. This is, however, only an optical analog of a quantum system, and it would be highly desirable to observe the manifestation of $\mathcal{PT}$ symmetry and the resulting properties also in a real, experimentally accessible, quantum system. Following a suggestion by Klaiman et al. [Phys. Rev. Lett. 101, 080402 (2008)], we investigate a $\mathcal{PT}$-symmetric arrangement of a Bose-Einstein condensate in a double-well potential, where in one well cold atoms are injected while in the other particles are extracted from the condensate. We investigate, in particular, the effects of the nonlinearity in the Gross-Pitaevskii equation on the $\mathcal{PT}$ properties of the condensate. To study these effects we analyze a simple one-dimensional model system in which the condensate is placed into two $\mathcal{PT}$-symmetric $\ensuremath{\delta}$-function traps. The analysis will serve as a useful guide for studies of the behavior of Bose-Einstein condensates in realistic $\mathcal{PT}$-symmetric double wells.
TL;DR: In this article, the metastability and decay of multiply-charged superflow in a ring-shaped atomic Bose-Einstein condensate was studied and it was shown that the supercurrent decays rapidly if the superflow speed exceeds a critical velocity in good agreement with numerical simulations.
Abstract: We study the metastability and decay of multiply-charged superflow in a ring-shaped atomic Bose-Einstein condensate. Supercurrent corresponding to a giant vortex with topological charge up to q=10 is phase-imprinted optically and detected both interferometrically and kinematically. We observe q=3 superflow persisting for up to a minute and clearly resolve a cascade of quantised steps in its decay. These stochastic decay events, associated with vortex-induced $2 \pi$ phase slips, correspond to collective jumps of atoms between discrete q values. We demonstrate the ability to detect quantised rotational states with > 99 % fidelity, which allows a detailed quantitative study of time-resolved phase-slip dynamics. We find that the supercurrent decays rapidly if the superflow speed exceeds a critical velocity in good agreement with numerical simulations, and we also observe rare stochastic phase slips for superflow speeds below the critical velocity.
TL;DR: In this paper, the authors extend the analysis of bilocal correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010) and derive new Bell-type inequalities based on the bilocality assumption in different scenarios, study their possible quantum violations, and analyze their resistance to experimental imperfections.
Abstract: Entanglement swapping is a process bywhich two initially independent quantum systems can become entangled and generate nonlocal correlations. To characterize such correlations, we compare them to those predicted by bilocal models, where systems that are initially independent are described by uncorrelated states. We extend in this paper the analysis of bilocal correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010)]. In particular, we derive new Bell-type inequalities based on the bilocality assumption in different scenarios, we study their possible quantum violations, and we analyze their resistance to experimental imperfections. The bilocality assumption, being stronger than Bell’s standard local causality assumption, lowers the requirements for the demonstration of quantumness in entanglement-swapping experiments.
TL;DR: In this article, an efficient quantum repeater protocol that uses coupled systems of quantum-dot spins and optical microcavities was proposed, in which the spatial entanglement of a photon system can be converted into polarization entenglement of electron spins.
Abstract: We present an efficient quantum repeater protocol that uses coupled systems of quantum-dot spins and optical microcavities, in which the spatial entanglement of a photon system can be converted into polarization entanglement of electron spins. The bit-flip and phase-flip errors on the polarization state of each qubit caused by noisy channels can be rejected, without resorting to additional qubits. Two remote parties can obtain the maximally entangled electron-spin state and store it deterministically after the transmission of photons, independent of the noise parameters. The transmission distance of photons will not be limited by the coherence time of memory units in the present protocol, unlike the previous atomic-ensemble-based quantum repeater protocols, and it can be applied directly in long-distance quantum-communication protocols.
TL;DR: In this paper, a scheme for measurement-device-independent quantum key distribution using phase and path or time encoding is presented, which employs simple encoding and decoding modules without relying on polarization maintenance or optical switches.
Abstract: Practical schemes for measurement-device-independent quantum key distribution using phase and path or time encoding are presented. In addition to immunity to existing loopholes in detection systems, our setup employs simple encoding and decoding modules without relying on polarization maintenance or optical switches. Moreover, by employing a modified sifting technique to handle the dead-time limitations in single-photon detectors, our scheme can be run with only two single-photon detectors. With a phase-post-selection technique, a decoy-state variant of our scheme is also proposed, whose key generation rate scales linearly with the channel transmittance.