Efficient Spin Injection into Silicon and the Role of the Schottky Barrier

Implementing spin functionalities in Si, and understanding the fundamental processes of spin injection and detection, are the main challenges in spintronics. Here we demonstrate large spin polarizations at room temperature, 34% in n-type and 10% in p-type degenerate Si bands, using a narrow Schottky and a SiO2 tunnel barrier in a direct tunneling regime. Furthermore, by increasing the width of the Schottky barrier in non-degenerate p-type Si, we observed a systematic sign reversal of the Hanle signal in the low bias regime. This dramatic change in the spin injection and detection processes with increased Schottky barrier resistance may be due to a decoupling of the spins in the interface states from the bulk band of Si, yielding a transition from a direct to a localized state assisted tunneling. Our study provides a deeper insight into the spin transport phenomenon, which should be considered for electrical spin injection into any semiconductor

Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarifie

Quantum non-malleability and authentication

In encryption, non-malleability is a highly desirable property: it ensures that adversaries cannot manipulate the plaintext by acting on the ciphertext. Ambainis, Bouda and Winter gave a definition of non-malleability for the encryption of quantum data. In this work, we show that this definition is too weak, as it allows adversaries to "inject" plaintexts of their choice into the ciphertext. We give a new definition of quantum non-malleability which resolves this problem. Our definition is expressed in terms of entropic quantities, considers stronger adversaries, and does not assume secrecy. Rather, we prove that quantum non-malleability implies secrecy; this is in stark contrast to the classical setting, where the two properties are completely independent. For unitary schemes, our notion of non-malleability is equivalent to encryption with a two-design (and hence also to the definition of Ambainis et al.). Our techniques also yield new results regarding the closely-related task of quantum authentication. We show that "total authentication" (a notion recently proposed by Garg, Yuen and Zhandry) can be satisfied with two-designs, a significant improvement over the eight-design construction of Garg et al. We also show that, under a mild adaptation of the rejection procedure, both total authentication and our notion of non-malleability yield quantum authentication as defined by Dupuis, Nielsen and Salvail.Comment: 20+13 pages, one figure. v2: published version plus extra material. v3: references added and update

(Pseudo) Random Quantum States with Binary Phase

We prove a quantum information-theoretic conjecture due to Ji, Liu and Song (CRYPTO 2018) which suggested that a uniform superposition with random \emph{binary} phase is statistically indistinguishable from a Haar random state. That is, any polynomial number of copies of the aforementioned state is within exponentially small trace distance from the same number of copies of a Haar random state. As a consequence, we get a provable elementary construction of \emph{pseudorandom} quantum states from post-quantum pseudorandom functions. Generating pseduorandom quantum states is desirable for physical applications as well as for computational tasks such as quantum money. We observe that replacing the pseudorandom function with a $(2t)$-wise independent function (either in our construction or in previous work), results in an explicit construction for \emph{quantum state $t$-designs} for all $t$. In fact, we show that the circuit complexity (in terms of both circuit size and depth) of constructing $t$-designs is bounded by that of $(2t)$-wise independent functions. Explicitly, while in prior literature $t$-designs required linear depth (for $t > 2$), this observation shows that polylogarithmic depth suffices for all $t$. We note that our constructions yield pseudorandom states and state designs with only real-valued amplitudes, which was not previously known. Furthermore, generating these states require quantum circuit of restricted form: applying one layer of Hadamard gates, followed by a sequence of Toffoli gates. This structure may be useful for efficiency and simplicity of implementation

Efficient and feasible state tomography of quantum many-body systems

We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for measuring a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary 2-designs, i.e., certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established techniques like optical super-lattices, laser speckles, and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. Combining our approach with tensor network methods - in particular the theory of matrix-product states - we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing in principle to perform tomography on large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing that no single-site addressing is needed at any stage of the scheme when implemented in optical lattice system

Determination of the characteristic directions of lossless linear optical elements

We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of the optical device. This formulation makes any actual computation of the characteristic directions amenable to pre-implemented numerical routines, thereby facilitating the decomposition of the transfer matrix into equivalent linear retarders and rotators according to the related Poincare equivalence theorem. The method is expected to be useful whenever the inverse problem of reconstruction of the internal state of a transparent medium from optical data obtained by tomographical methods is an issue.Comment: Replaced with extended version as published in JM

Decoupling with unitary approximate two-designs

Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R, i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems, which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate 2-designs are appropriate for decoupling even if the dimension of this system is large.Comment: Published versio

Strongly anisotropic spin relaxation in graphene/transition metal dichalcogenide heterostructures at room temperature

Graphene has emerged as the foremost material for future two-dimensional spintronics due to its tuneable electronic properties. In graphene, spin information can be transported over long distances and, in principle, be manipulated by using magnetic correlations or large spin-orbit coupling (SOC) induced by proximity effects. In particular, a dramatic SOC enhancement has been predicted when interfacing graphene with a semiconducting transition metal dechalcogenide, such as tungsten disulphide (WS$_2$). Signatures of such an enhancement have recently been reported but the nature of the spin relaxation in these systems remains unknown. Here, we unambiguously demonstrate anisotropic spin dynamics in bilayer heterostructures comprising graphene and WS$_2$. By using out-of-plane spin precession, we show that the spin lifetime is largest when the spins point out of the graphene plane. Moreover, we observe that the spin lifetime varies over one order of magnitude depending on the spin orientation, indicating that the strong spin-valley coupling in WS$_2$ is imprinted in the bilayer and felt by the propagating spins. These findings provide a rich platform to explore coupled spin-valley phenomena and offer novel spin manipulation strategies based on spin relaxation anisotropy in two-dimensional materials

Tight informationally complete quantum measurements

We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows "painless" quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.Comment: 20 pages. Final versio