
Konig, R., & Smith, G. (2014). The Entropy Power Inequality for Quantum Systems. IEEE Trans. Inf. Theory, 60(3), 1536–1548.
Abstract: When two independent analog signals, X and Y are added together giving Z = X + Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the entropy power inequality (EPI), which states that e(2H(Z)) >= e(2H(X)) + e(2H(Y)), gives a very tight restriction on the entropy of Z. This inequality has found many applications in information theory and statistics. The quantum analogue of adding two random variables is the combination of two independent bosonic modes at a beam splitter. The purpose of this paper is to give a detailed outline of the proof of two separate generalizations of the EPI to the quantum regime. Our proofs are similar in spirit to the standard classical proofs of the EPI, but some new quantities and ideas are needed in the quantum setting. In particular, we find a new quantum de Bruijin identity relating entropy production under diffusion to a divergencebased quantum Fisher information. Furthermore, this Fisher information exhibits certain convexity properties in the context of beam splitters.
Keywords: Quantum information; entropypower inequality; differential entropy; Gaussian channels


Childs, A. M., & Wiebe, N. (2013). Product formulas for exponentials of commutators. J. Math. Phys., 54(6), 25 pp.
Abstract: We provide a recursive method for systematically constructing product formula approximations to exponentials of commutators, giving approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate unitary exponentials of (possibly nested) commutators using exponentials of the elementary operators, and we upper bound the number of elementary exponentials needed to implement the desired operation within a given error tolerance. By presenting an algorithm for quantum search using evolution according to a commutator, we show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. Finally, we discuss applications of our product formulas to quantum control and to implementing anticommutators, providing new methods for simulating manybody interaction Hamiltonians. (C) 2013 AIP Publishing LLC.


Veitch, V., Mousavian, S. A. H., Gottesman, D., & Emerson, J. (2014). The resource theory of stabilizer quantum computation. New J. Phys., 16, 32 pp.
Abstract: Recent results on the nonuniversality of fault tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, that is relevant for faulttolerant stabilizer computation. We introduce two quantitative measuresmonotonesfor the amount of nonstabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a longstanding open question of whether the degree of negativity in a quasiprobability representation is an operationally meaningful indicator of quantum behavior.


Dengis, J., Konig, R., & Pastawski, F. (2014). An optimal dissipative encoder for the toric code. New J. Phys., 16, 11 pp.
Abstract: We consider the problem of preparing specific encoded resource states for the toric code by local, timeindependent interactions with a memoryless environment. We propose the construction of such a dissipative encoder which converts product states to topologically ordered ones while preserving logical information. The corresponding Liouvillian is made up of four local Lindblad operators. For a qubit lattice of size L x L, we show that this process prepares encoded states in time O(L), which is optimal. This scaling compares favorably with known local unitary encoders for the toric code which take time of order Omega(L2) and require active timedependent control.


Gheorghiu, V. (2014). Standard form of qudit stabilizer groups. Phys. Lett. A, 378(56), 505–509.
Abstract: We investigate stabilizer codes with carrier qudits of equal dimension D, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding stabilizer, and this implies that the code and its stabilizer are dual to each other. We also show that any qudit stabilizer can be put in a canonical, or standard, form using a series of Clifford gates, and we provide an explicit efficient algorithm for doing this.. Our work generalizes known results that were valid only for prime dimensional systems and may be useful in constructing efficient encoding/decoding quantum circuits for qudit stabilizer codes and better qudit quantum error correcting codes. (C) 2013 Elsevier B.V. All rights reserved.


SaiToh, A., Rahimi, R., & Nakahara, M. (2014). A quantum genetic algorithm with quantum crossover and mutation operations. Quantum Inf. Process., 13(3), 737–755.
Abstract: In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm that has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.
Keywords: Genetic algorithm; Quantum computing; Computational complexity


M Khoshnegar, A. J.  S., M H Ansari and A H Majedi. (2014). Toward tripartite hybrid entanglement in quantum dot molecules. New J. Phys., 16(023019).
Abstract: Establishing the hybrid entanglement among a growing amount of matter and photonic quantum bits is necessary for scalable quantum computation and longdistance quantum communication. Here we demonstrate that charged excitonic complexes forming in strongly correlated quantum dot molecules are able to generate tripartite hybrid entanglement under proper carrier quantization. The mixed orbitals of the molecule construct multilevel ground states with submeV hole tunneling energy and relatively large electron hybridization energy. We show that appropriate size and interdot spacing keeps the electron particle weakly localized, opening extra recombination channels by correlating groundstate excitons. This allows for creation of higher order entangled states. Nontrivial hole tunneling energy, renormalized by multiparticle interactions, facilitates the realization of the energy coincidence among only certain components of the molecule optical spectrum. This translates to the emergence of favorable spectral components in a multibody excitonic complex which sustain principal oscillator strengths throughout the electric fieldinduced hole tunneling process. We particularly analyze whether the level broadening of favorable spin configurations could be manipulated to eliminate the distinguishability of photons.


Motzoi, F., & Wilhelm, F. K. (2013). Improving frequency selection of driven pulses using derivativebased transition suppression. Phys. Rev. A, 88(6), 15 pp.
Abstract: Many techniques in quantum control rely on frequency separation as a means for suppressing unwanted couplings. In its simplest form, the mechanism relies on the low bandwidth of control pulses of long duration. Here we perform a higherorder quantummechanical treatment that allows for higher precision and shorter times. In particular, we identify three kinds of offresonant effects: (i) simultaneous unwanted driven couplings (e. g., due to drive crosstalk), (ii) additional (initially undriven) transitions such as those in an infinite ladder system, and (iii) sideband frequencies of the driving wave form such as we find in corrections to the rotatingwave approximation. With a framework that is applicable to all three cases, in addition to the known adiabatic error responsible for a shift of the energy levels we typically see in the spectroscopy of such systems, we derive error terms in a controlled expansion corresponding to higherorder adiabatic effects and diabatic excitations. We show, by also expanding the driving wave form in a basis of different order derivatives of a trial function (typically a Gaussian) these different error terms can be corrected for in a systematic way, hence strongly improving quantum control of systems with dense spectra.


Mandal, S., Koroleva, V. D. M., Borneman, T. W., Song, Y. Q., & Hurlimann, M. D. (2013). Axismatching excitation pulses for CPMGlike sequences in inhomogeneous fields. J. Magn. Reson., 237, 1–10.
Abstract: The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. Here we introduce a new class of excitation pulses, socalled axismatching excitation pulses, that optimize the response for a given refocusing pulse. These new excitation pulses are tailored to the refocusing pulses and take their imperfections into account. Rather than generating purely transverse magnetization, these pulses are designed to generate magnetization pointing along the axis of the effective rotation of the refocusing cycle. This approach maximizes the CPMG component and minimizes the CP component of the signal. Replacing a standard 90 degrees pulse with a new excitation pulse matched to the 180 degrees refocusing pulse increases the signal bandwidth and improves the echo amplitudes by 30% in inhomogeneous fields in comparison to the standard CPMG sequence. Larger gains are obtained with more advanced refocusing pulses. Recent work demonstrated that it is possible to increase the signal to noise ratio (SNR) of individual echoes by more than a factor of 1.5 (in power units) without increasing the duration or amplitude of the refocusing pulses. This was achieved by replacing the standard 180 degrees refocusing pulse by a short phase alternating pulse and the standard 90 degrees excitation pulse by a broadband excitation pulse. We show here that with suitable axismatching excitation pulses, the SNR further increases by over a factor of 2. We discuss the underlying theory and present several practical implementations of purely phase modulated axismatching excitation pulses for a number of different refocusing pulses that were derived using methods of optimal control. To gain the full benefit of these new excitation pulses, it is essential to replace the standard phase cycling scheme based on 180 degrees phase shifts by a new scheme involving phase inversion. We tested the new pulses experimentally and observe excellent agreement with the theoretical expectations. We also demonstrate that an additional benefit of axismatching excitation pulses is the decrease of the transient that appears in the amplitudes of the first few echoes, thus enabling better measurements of short relaxation times. (C) 2013 Elsevier Inc. All rights reserved.
Keywords: CPMG; Inhomogeneous fields; Excitation pulse


Friedland, S., Gheorghiu, V., & Gour, G. (2013). Universal Uncertainty Relations. Phys. Rev. Lett., 111(23), 5 pp.
Abstract: Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs entropic measures to quantify the lack of knowledge associated with measuring noncommuting observables. However, there is no fundamental reason for using entropies as quantifiers; any functional relation that characterizes the uncertainty of the measurement outcomes defines an uncertainty relation. Starting from a very reasonable assumption of invariance under mere relabeling of the measurement outcomes, we show that Schurconcave functions are the most general uncertainty quantifiers. We then discover a finegrained uncertainty relation that is given in terms of the majorization order between two probability vectors, significantly extending a majorizationbased uncertainty relation first introduced in M. H. Partovi, Phys. Rev. A 84, 052117 (2011). Such a vectortype uncertainty relation generates an infinite family of distinct scalar uncertainty relations via the application of arbitrary uncertainty quantifiers. Our relation is therefore universal and captures the essence of uncertainty in quantum theory.


Eftekharian, A., Atikian, H., Akhlaghi, M. K., Salim, A. J., & Majedi, A. H. (2013). Quantum ground state effect on fluctuation rates in nanopatterned superconducting structures. Appl. Phys. Lett., 103(24), 4 pp.
Abstract: In this Letter, we present a theoretical model with experimental verifications to describe the abnormal behaviors of the measured fluctuation rates occurring in nanopatterned superconducting structures below the critical temperature. In the majority of previous works, it is common to describe the fluctuation rate by defining a fixed ground state or initial state level for the singularities (vortex or vortexantivortex pairs), and then employing the wellknown rate equations to calculate the liberation rates. Although this approach gives an acceptable qualitative picture, without utilizing free parameters, all the models have been inadequate in describing the temperature dependence of the rate for a fixed width or the width dependence of the rate for a fixed temperature. Here, we will show that by defining a currentcontrolled ground state level for both the vortex and vortexantivortex liberation mechanisms, the dynamics of these singularities are described for a wide range of temperatures and widths. According to this study, for a typical strip width, not only is the vortexantivortex liberation higher than the predicted rate, but also quantum tunneling is significant in certain conditions and can not be neglected. (C) 2013 AIP Publishing LLC.


OnumaKalu, M., Mann, R. B., & MartinMartinez, E. (2013). Mode invisibility and singlephoton detection. Phys. Rev. A, 88(6), 11 pp.
Abstract: We propose a technique to probe the quantum state of light in an optical cavity without significantly altering it. We minimize the interaction of the probe with the field by arranging a setting where the largest contribution to the transition probability is canceled. We show that we obtain a very good resolution to measure photon population differences between two given Fock states by means of atomic interferometry.


Johnston, N. (2013). Separability from spectrum for qubitqudit states. Phys. Rev. A, 88(6), 5 pp.
Abstract: The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states rho with the property that Udagger rho U is separable for all unitary matrices U. This problem has been solved when the local dimensions m and n satisfy m = 2 and n <= 3. We solve all remaining qubitqudit cases (i.e., when m = 2 and n >= 4 is arbitrary). In all of these cases we show that a state is separable from spectrum if and only if Udagger rho U has positive partial transpose for all unitary matrices U. This equivalence is in stark contrast with the usual separability problem, where a state having positive partial transpose is a strictly weaker property than it being separable.


Childs, A. M., Leung, D., Mancinska, L., & Ozols, M. (2013). Interpolatability distinguishes LOCC from separable von Neumann measurements. J. Math. Phys., 54(11), 10 pp.
Abstract: Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations. (C) 2013 AIP Publishing LLC.


Kliuchnikov, V., & Maslov, D. (2013). Optimization of Clifford circuits. Phys. Rev. A, 88(5), 7 pp.
Abstract: We study synthesis of optimal Clifford circuits and apply the results to peephole optimization of quantum circuits. We report optimal circuits for all Clifford operations with up to four inputs. We perform peephole optimization of Clifford circuits with up to 40 inputs found in the literature, and demonstrate a reduction in the number of gates by about 50%. We extend our methods to the synthesis of optimal linear reversible circuits, partially specified Clifford unitaries, and optimal Clifford circuits with five inputs up to inputoutput permutation. The results find their application in randomized benchmarking protocols, quantum error correction, and quantum circuit optimization.


