Physics

We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical components, allowing the former to be of lower dimension than the secret itself. We show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods. We further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall perfect QSS scheme, and that examples of such schemes (which we construct) can have the smallest quantum and classical share components possible for their access structures, something provably not achievable using perfect underlying schemes. Our construction has significant potential for being adapted to other QSS schemes based on stabiliser codes.

We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.

Ancilla post-selection is a common means of achieving fault-tolerance in quantum error-correction. However, it can lead to additional data errors due to movement or wait operations. Alternatives to post-selection may achieve lower overall failure rates due to avoiding such errors. We present numerical simulation results comparing the logical error rates for the fault-tolerant [[7,1,3]] Steane code using techniques of ancilla verification vs. the newer method of ancilla decoding, as described in . We simulate QEC procedures in which rhe possibility of ancilla verification failures requires the creation and storage of additional ancillas and/or additional waiting of the data until a new ancilla can be created. We find that the decoding method, which avoids verification failures, is advantageous in terms of overall error rate in various cases, even when measurement operations are no slower than others. We analyze the effect of different classes of physical error on the relative performance of these two methods.

We derive lower limits on the inefficiency and classical communication costs of dilution between two-term bipartite pure states that are partially entangled. We first calculate explicit relations between the allowable error and classical communication costs of entanglement dilution using the protocol of [1] and then consider a two-stage dilution from singlets with this protocol followed by some unknown protocol for conversion between partially entangled states. Applying the lower bounds on classical communication and inefficiency of [2], [3] to this two-stage protocol, we derive bounds for the unknown protocol. In addition we derive analogous (but looser) bounds for general pure states.

We describe various results related to the random distillation of multiparty entangled states -that is, conversion of such states into entangled states shared between fewer parties, where those parties are not predetermined. In previous work [1] we showed that certain output states (namely Einstein-Podolsky-Rosen (EPR) pairs) could be reliably acquired from a prescribed initial multipartite state (namely the W state |W = 1 √ 3 (|100 + |010 + |001 )) via random distillation that could not be reliably created between predetermined parties. Here we provide a more rigorous definition of what constitutes "advantageous" random distillation. We show that random distillation is always advantageous for W -class three-qubit states (but only sometimes for Greenberger-Horne-Zeilinger (GHZ)-class states). We show that the general class of multiparty states known as symmetric Dicke states can be readily converted to many other states in the class via random distillation. Finally we show that random distillation is provably not advantageous in the limit of multiple copies of pure states.

The security of a high speed quantum key distribution system with finite detector dead time  is analyzed. When the transmission rate becomes higher than the maximum count rate of the individual detectors (1/), security issues affect the algorithm for sifting bits. Analytical calculations and numerical simulations of the Bennett-Brassard BB84 protocol are performed. We study Rogers et al.'s protocol (introduced in "Detector dead-time effects and paralyzability in high-speed quantum key distribution," New J. Phys. 9 (2007) 319) in the presence of an active eavesdropper Eve who has the power to perform an intercept-resend attack. It is shown that Rogers et al."s protocol is no longer secure. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver"s end.

We introduce a new multiparty cryptographic protocol, which we call 'entanglement sharing schemes', wherein a dealer retains half of a maximally-entangled bipartite state and encodes the other half into a multipartite state that is distributed among multiple players. In a close analogue to quantum secret sharing, some subsets of players can recover maximal entanglement with the dealer whereas other subsets can recover no entanglement (though they may retain classical correlations with the dealer). We find a lower bound on the share size for such schemes and construct two non-trivial examples based on Shor's [[9, 1, 3]] and the [[4, 2, 2]] stabilizer code; we further demonstrate how other examples may be obtained from quantum error correcting codes through classical encryption. Finally, we demonstrate that entanglement sharing schemes can be applied to characterize leaked information in quantum ramp secret sharing.

Transport measurements were made on four-terminal devices fabricated from InSb/Al x In 1-x Sb quantum well structures at temperatures from 1.5 to 300K. Negative bend resistance, which is characteristic of ballistic transport, was observed in devices of channel widths 0.2 or 0.5 µm. We have improved upon the existing implementations of R-matrix theory in device physics by introducing boundary conditions that dramatically speed convergence. By comparison with R-matrix calculations, we show that the experimental observations are consistent with quantum coherent transport.

We discuss the theory of cooling electrons in solid-state devices via "evaporative emission." Our model is based on filtering electron subbands in a quantum-wire device. When incident electrons in a higher-energy subband scatter out of the initial electron distribution, the system equilibrates to a different chemical potential and temperature than those of the incident electron distribution. We show that this re-equilibration can cause considerable cooling of the system. We discuss how the device geometry affects the final electron temperatures, and consider factors relevant to possible experiments. We demonstrate that one can therefore induce substantial electron cooling due to quantum effects in a room-temperature device. The resulting cooled electron population could be used for photodetection of optical frequencies corresponding to thermal energies near room temperature.

Negative bend resistance is a signature of ballistic transport in low-dimension semiconductor devices. We calculate the bend resistance in 4-terminal devices using R-matrix theory. R-matrix theory is a technique first introduced in nuclear physics and recently shown to be a useful tool for calculating transport properties of solid-state devices. We have improved upon the existing implementations of R-matrix theory in device physics by applying a variational basis function approach that dramatically improves the rate of convergence of transmission coefficients. We have also developed a method for calculating transmission coefficients of a device in a nonzero magnetic field. We calculate bend resistance in 4-terminal devices. r

We discuss the theory of cooling electrons in solid-state devices via "evaporative emission." Our model is based on filtering electron subbands in a quantum-wire device. When incident electrons in a higher-energy subband scatter out of the initial electron distribution, the system equilibrates to a different chemical potential and temperature than those of the incident electron distribution. We show that this re-equilibration can cause considerable cooling of the system. We discuss how the device geometry affects the final electron temperatures, and consider factors relevant to possible experiments. We demonstrate that one can therefore substantial electron cooling due to quantum effects in a room-temperature device. The resulting cooled electron population could be used for photo-detection of optical frequencies corresponding to thermal energies near room temperature.

Using model interaction Hamiltonians for both electrons and phonons and Green's function formalism for ballistic transport, we have studied the thermal conductance and the thermoelectric properties of graphene nanoribbons (GNR), GNR junctions and periodic superlattices. Among our findings we have established the role that interfaces play in determining the thermoelectric response of GNR systems both across single junctions and in periodic superlattices. In general, increasing the number of interfaces in a single GNR system increases the peak ZT values that are thus maximized in a periodic superlattice. Moreover, we proved that the thermoelectric behavior is largely controlled by the width of the narrower component of the junction. Finally, we have demonstrated that chevron-type GNRs recently synthesized should display superior thermoelectric properties.