Practical implementation of mutually unbiased bases using quantum circuits

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.Comment: 5 pages, 2 color figures. Comments welcome

Effect of pressure cycling on Iron: Signatures of an electronic instability and unconventional superconductivity

High pressure electrical resistivity and x-ray diffraction experiments have been performed on Fe single crystals. The crystallographic investigation provides direct evidence that in the martensitic $bcc \rightarrow hcp$ transition at 14 GPa the $\lbrace 110\rbrace_{bcc}$ become the $\lbrace 002\rbrace_{hcp}$ directions. During a pressure cycle, resistivity shows a broad hysteresis of 6.5 GPa, whereas superconductivity, observed between 13 and 31 GPa, remains unaffected. Upon increasing pressure an electronic instability, probably a quantum critical point, is observed at around 19 GPa and, close to this pressure, the superconducting $T_{c}$ and the isothermal resistivity ($0<T<300\,$K) attain maximum values. In the superconducting pressure domain, the exponent $n = 5/3$ of the temperature power law of resistivity and its prefactor, which mimics $T_{c}$, indicate that ferromagnetic fluctuations may provide the glue for the Cooper pairs, yielding unconventional superconductivity

Superconductivity without Fe or Ni in the phosphides BaIr2P2 and BaRh2P2

Heat capacity, resistivity, and magnetic susceptibility measurements confirm bulk superconductivity in single crystals of BaIr$_2$P$_2$ (T$_c$=2.1K) and BaRh$_2$P$_2$ (T$_c$ = 1.0 K). These compounds form in the ThCr$_2$Si$_2$ (122) structure so they are isostructural to both the Ni and Fe pnictides but not isoelectronic to either of them. This illustrates the importance of structure for the occurrence of superconductivity in the 122 pnictides. Additionally, a comparison between these and other ternary phosphide superconductors suggests that the lack of interlayer $P-P$ bonding favors superconductivity. These stoichiometric and ambient pressure superconductors offer an ideal playground to investigate the role of structure for the mechanism of superconductivity in the absence of magnetism.Comment: Published in Phys Rev B: Rapid Communication

Fermi surface instabilities in CeRh2Si2 at high magnetic field and pressure

We present thermoelectric power (TEP) studies under pressure and high magnetic field in the antiferromagnet CeRh2Si2 at low temperature. Under magnetic field, large quantum oscillations are observed in the TEP, S(H), in the antiferromagnetic phase. They suddenly disappear when entering in the polarized paramagnetic (PPM) state at Hc pointing out an important reconstruction of the Fermi surface (FS). Under pressure, S/T increases strongly of at low temperature near the critical pressure Pc, where the AF order is suppressed, implying the interplay of a FS change and low energy excitations driven by spin and valence fluctuations. The difference between the TEP signal in the PPM state above Hc and in the paramagnetic state (PM) above Pc can be explained by different FS. Band structure calculations at P = 0 stress that in the AF phase the 4f contribution at the Fermi level (EF) is weak while it is the main contribution in the PM domain. By analogy to previous work on CeRu2Si2, in the PPM phase of CeRh2Si2 the 4f contribution at EF will drop.Comment: 10 pages, 13 figure

Heavy Fermion superconductor CeCu2_2Si2_2 under high pressure: multiprobing the valence crossover

The first heavy fermion superconductor CeCu$_2$Si$_2$ has not revealed all its striking mysteries yet. At high pressures, superconductivity is supposed to be mediated by valence fluctuations, in contrast to ambient pressure, where spin fluctuations most likely act as pairing glue. We have carried out a multiprobe (electric transport, thermopower, ac specific heat, Hall and Nernst effects) experiment up to $7 \text{GPa}$ on a high quality CeCu$_2$Si$_2$ single crystal. Reliable resistivity data reveal for the first time a scaling behavior close to the supposed valence transition, and allow to locate the critical end point at $4.5\pm0.2 \text{GPa}$ and a slightly negative temperature. In the same pressure region, remarkable features have also been detected in the other physical properties, acting as further signatures of the Ce valence crossover and the associated critical fluctuations.Comment: 13 pages, 14 figure

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc

Wilson ratio in Yb-substituted CeCoIn5

We have investigated the effect of Yb substitution on the Pauli limited, heavy fermion superconductor, CeCoIn$_5$. Yb acts as a non-magnetic divalent substituent for Ce throughout the entire doping range, equivalent to hole doping on the rare earth site. We found that the upper critical field in (Ce,Yb)CoIn$_5$ is Pauli limited, yet the reduced (H,T) phase diagram is insensitive to disorder, as expected in the purely orbitally limited case. We use the Pauli limiting field, the superconducting condensation energy and the electronic specific heat coefficient to determine the Wilson ratio ($R_{W}$), the ratio of the specific heat coefficient to the Pauli susceptibility in CeCoIn$_5$. The method is applicable to any Pauli limited superconductor in the clean limit.Comment: 5 pages, 1 table, 4 figure

Superconducting phase diagram of the filled skuterrudite PrOs4Sb12

We present new measurements of the specific heat of the heavy fermion superconductor PrOs4Sb12, on a sample which exhibits two sharp distinct anomalies at Tc1= 1.89K and Tc2= 1.72K. They are used to draw a precise magnetic field-temperature superconducting phase diagram of PrOs4Sb12 down to 350 mK. We discuss the superconducting phase diagram of PrOs4Sb12 and its possible relation with an unconventional superconducting order parameter. We give a detailed analysis of Hc2(T), which shows paramagnetic limitation (a support for even parity pairing) and multiband effects

Fermi-surface topology of the iron pnictide LaFe2_2P2_2

We report on a comprehensive de Haas--van Alphen (dHvA) study of the iron pnictide LaFe$_2$P$_2$. Our extensive density-functional band-structure calculations can well explain the measured angular-dependent dHvA frequencies. As salient feature, we observe only one quasi-two-dimensional Fermi-surface sheet, i.e., a hole-like Fermi-surface cylinder around $\Gamma$, essential for $s_\pm$ pairing, is missing. In spite of considerable mass enhancements due to many-body effects, LaFe$_2$P$_2$ shows no superconductivity. This is likely caused by the absence of any nesting between electron and hole bands.Comment: 5 pages, 4 figure

Direct observation of the quantum critical point in heavy fermion CeRhSi3_3

We report on muon spin rotation studies of the noncentrosymmetric heavy fermion antiferromagnet CeRhSi$_3$. A drastic and monotonic suppression of the internal fields, at the lowest measured temperature, was observed upon an increase of external pressure. Our data suggest that the ordered moments are gradually quenched with increasing pressure, in a manner different from the pressure dependence of the N\'eel temperature. At \unit{23.6}{kbar}, the ordered magnetic moments are fully suppressed via a second-order phase transition, and $T_{\rm{N}}$ is zero. Thus, we directly observed the quantum critical point at \unit{23.6}{kbar} hidden inside the superconducting phase of CeRhSi$_3$