- Aug 22 2017 quant-ph arXiv:1708.06144v1In this work, we demonstrate a new way to perform classical multiparty computing amongst parties with limited computational resources. Our method harnesses quantum resources to increase the computational power of the individual parties. We show how a set of clients restricted to linear classical processing are able to jointly compute a non-linear multivariable function that lies beyond their individual capabilities. The clients are only allowed to perform classical XOR gates and single-qubit gates on quantum states. We also examine the type of security that can be achieved in this limited setting. Finally, we provide a proof-of-concept implementation using photonic qubits, that allows four clients to compute a specific example of a multiparty function, the pairwise AND.
- We consider the problem of quantum state certification, where one is given $n$ copies of an unknown $d$-dimensional quantum mixed state $\rho$, and one wants to test whether $\rho$ is equal to some known mixed state $\sigma$ or else is $\epsilon$-far from $\sigma$. The goal is to use notably fewer copies than the $\Omega(d^2)$ needed for full tomography on $\rho$ (i.e., density estimation). We give two robust state certification algorithms: one with respect to fidelity using $n = O(d/\epsilon)$ copies, and one with respect to trace distance using $n = O(d/\epsilon^2)$ copies. The latter algorithm also applies when $\sigma$ is unknown as well. These copy complexities are optimal up to constant factors.
- Aug 22 2017 quant-ph arXiv:1708.05901v1We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely solve this problem in the two-qubit case and we derive a large family of new necessary conditions on the spectra in arbitrary dimensions. We also establish a natural duality relationship with the set of absolutely separable states, and we completely characterize witnesses (i.e., separating hyperplanes) of that set when one of the local dimensions is 2.
- Aug 22 2017 cs.CC arXiv:1708.05786v1We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided error using $\widetilde{O}(n^{3/4}/\epsilon^2)$ queries. This improves on the best adaptive $O(n/\epsilon)$-query algorithm from Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova and Seshadhri when $1/\epsilon \ll n^{1/4}$. Combined with the $\widetilde{\Omega}(n)$-query lower bound for non-adaptive algorithms with one-sided error of [CWX17, BCPRS17], we conclude that adaptivity helps for the testing of unateness with one-sided error. A crucial component of our algorithm is a new subroutine for finding bi-chromatic edges in the Boolean hypercube called adaptive edge search.
- Zero-field nuclear magnetic resonance (NMR) provides complementary analysis modalities to those of high-field NMR and allows for ultra-high-resolution spectroscopy and measurement of untruncated spin-spin interactions. Unlike for the high-field case, however, universal quantum control -- the ability to perform arbitrary unitary operations -- has not been experimentally demonstrated in zero-field NMR. This is because the Larmor frequency for all spins is identically zero at zero field, making it challenging to individually address different spin species. We realize a composite-pulse technique for arbitrary independent rotations of $^1$H and $^{13}$C spins in a two-spin system. Quantum-information-inspired randomized benchmarking and state tomography are used to evaluate the quality of the control. We experimentally demonstrate single-spin control for $^{13}$C with an average gate fidelity of $0.9960(2)$ and two-spin control via a controlled-not (CNOT) gate with an estimated fidelity of $0.99$. The combination of arbitrary single-spin gates and a CNOT gate is sufficient for universal quantum control of the nuclear spin system. The realization of complete spin control in zero-field NMR is an essential step towards applications to quantum simulation, entangled-state-assisted quantum metrology, and zero-field NMR spectroscopy.
- A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. However, the existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correcting codes and the generalized shadow inequalities, we obtain new bounds on the existence of AME states in higher dimensions. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation.
- Aug 22 2017 quant-ph arXiv:1708.06208v1We study the behavior of non-Markovianity with respect to the localization of the initial environmental state. The "amount" of non-Markovianity is measured using divisibility and distinguishability as indicators, employing several schemes to construct the measures. The system used is a qubit coupled to an environment modeled by an Ising spin chain kicked by ultra-short pulses of a magnetic field. In the integrable regime, non-Markovianity and localization do not have a simple relation, but as the chaotic regime is approached, simple relations emerge, which we explore in detail. We also study the non-Markovianity measures in the space of the parameters of the spin coherent states and point out that the pattern that appears is robust under the choice of the interaction Hamiltonian but does not have a KAM-like phase-space structure.
- Aug 22 2017 cs.RO arXiv:1708.06343v1
- Aug 22 2017 hep-th arXiv:1708.06342v1
- Aug 22 2017 math.AG arXiv:1708.06340v1
- Aug 22 2017 hep-th arXiv:1708.06339v1
- Aug 22 2017 stat.ME arXiv:1708.06337v1
- Aug 22 2017 cond-mat.str-el arXiv:1708.06335v1
- Aug 22 2017 cond-mat.mes-hall physics.app-ph arXiv:1708.06331v1
- Aug 22 2017 physics.optics physics.class-ph arXiv:1708.06330v1
- Aug 22 2017 math.AP arXiv:1708.06329v1
- Aug 22 2017 hep-th arXiv:1708.06328v1
- Aug 22 2017 hep-th arXiv:1708.06327v1
- Aug 22 2017 hep-ph arXiv:1708.06326v1
- Aug 22 2017 math.AG arXiv:1708.06325v1
- Aug 22 2017 nucl-th arXiv:1708.06321v1
- Aug 22 2017 cs.CV arXiv:1708.06320v1
- Aug 22 2017 math.DG arXiv:1708.06316v1
- Aug 22 2017 physics.flu-dyn astro-ph.EP arXiv:1708.06314v1
- Aug 22 2017 cs.NI arXiv:1708.06313v1
- Aug 22 2017 cs.LO arXiv:1708.06312v1
- Aug 22 2017 physics.ins-det arXiv:1708.06311v1
- Aug 22 2017 cs.SI arXiv:1708.06309v1
- Aug 22 2017 cs.CR arXiv:1708.06308v1
- Aug 22 2017 math.AP arXiv:1708.06307v1
- Aug 22 2017 math.NA arXiv:1708.06306v1
- Aug 22 2017 cs.RO arXiv:1708.06301v1
- Aug 22 2017 math.AP arXiv:1708.06300v1
- Aug 22 2017 cs.CV arXiv:1708.06297v1
- Aug 22 2017 math.PR arXiv:1708.06296v1
- Aug 22 2017 math.LO arXiv:1708.06295v1
- Aug 22 2017 math.AP arXiv:1708.06294v1