Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes

It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies to codes which recover the message exactly. Naively, one might expect that correcting errors to very high fidelity would only allow small violations of this bound. This intuition is incorrect: in this paper we describe quantum error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors with fidelity exponentially close to 1, at the price of increasing the size of the registers (i.e., the coding alphabet). This demonstrates a sharp distinction between exact and approximate quantum error correction. The codes have the property that any $t$ components reveal no information about the message, and so they can also be viewed as error-tolerant secret sharing schemes. The construction has several interesting implications for cryptography and quantum information theory. First, it suggests that secret sharing is a better classical analogue to quantum error correction than is classical error correction. Second, it highlights an error in a purported proof that verifiable quantum secret sharing (VQSS) is impossible when the number of cheaters t is n/4. More generally, the construction illustrates a difference between exact and approximate requirements in quantum cryptography and (yet again) the delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure

The Business of Being Good: CRM Strategies and For-Profit Organizations

Many studies have measured the impact of cause related marketing (CRM) strategies on non-profit organizations, however few have been able to measure the impact that these strategies can have on the for-profit organizations employing them. This study hypothesizes that a co-branded CRM strategy will have greater benefits for a for-profit organization than will a jointly-branded strategy or no strategy at all. This hypothesis was tested using two studies, both with a 2x3 factorial design for firms with both a positive and negative brand reputation. It was found that, for an organization with a negative image, consumers viewed the organization more positively when they employed a co-branding strategy. It was also found that the consumer was likely to donate more to a cause supported by the firm with a negative image when they used a co-branded strategy as opposed to a jointly-branded strategy. Alternatively, firms with a positive image generated more donations for a cause through a jointly-branded strategy

From Pine Cones to Read Clouds: Rescaffolding the Megagenome of Sugar Pine (Pinus lambertiana).

We investigate the utility and scalability of new read cloud technologies to improve the draft genome assemblies of the colossal, and largely repetitive, genomes of conifers. Synthetic long read technologies have existed in various forms as a means of reducing complexity and resolving repeats since the outset of genome assembly. Recently, technologies that combine subhaploid pools of high molecular weight DNA with barcoding on a massive scale have brought new efficiencies to sample preparation and data generation. When combined with inexpensive light shotgun sequencing, the resulting data can be used to scaffold large genomes. The protocol is efficient enough to consider routinely for even the largest genomes. Conifers represent the largest reference genome projects executed to date. The largest of these is that of the conifer Pinus lambertiana (sugar pine), with a genome size of 31 billion bp. In this paper, we report on the molecular and computational protocols for scaffolding the P. lambertiana genome using the library technology from 10× Genomics. At 247,000 bp, the NG50 of the existing reference sequence is the highest scaffold contiguity among the currently published conifer assemblies; this new assembly's NG50 is 1.94 million bp, an eightfold increase

Alien Registration- Crepeau, Armand (Biddeford, York County)

https://digitalmaine.com/alien_docs/1777/thumbnail.jp

On the Tropicalization of Lines onto Tropical Quadrics

Tropical geometry uses the minimum and addition operations to consider tropical versions of the curves, surfaces, and more generally the zero set of polynomials, called varieties, that are the objects of study in classical algebraic geometry. One known result in classical geometry is that smooth quadric surfaces in three-dimensional projective space, $\mathbb{P}^3$, are doubly ruled, and those rulings form a disjoint union of conics in $\mathbb{P}^5$. We wish to see if the same result holds for smooth tropical quadrics. We use the Fundamental Theorem of Tropical Algebraic Geometry to outline an approach to studying how lines lift onto a tropical quadric, which is necessary for understanding what lines are on smooth tropical quadrics and their structure. We also provide suggestions of how computational tools can be used to implement the approach

Authentication of Quantum Messages

Authentication is a well-studied area of classical cryptography: a sender S and a receiver R sharing a classical private key want to exchange a classical message with the guarantee that the message has not been modified by any third party with control of the communication line. In this paper we define and investigate the authentication of messages composed of quantum states. Assuming S and R have access to an insecure quantum channel and share a private, classical random key, we provide a non-interactive scheme that enables S both to encrypt and to authenticate (with unconditional security) an m qubit message by encoding it into m+s qubits, where the failure probability decreases exponentially in the security parameter s. The classical private key is 2m+O(s) bits. To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs. We also show that any scheme to authenticate quantum messages must also encrypt them. (In contrast, one can authenticate a classical message while leaving it publicly readable.) This has two important consequences: On one hand, it allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. On the other hand, we use it to show that digitally signing quantum states is impossible, even with only computational security.Comment: 22 pages, LaTeX, uses amssymb, latexsym, time

The NFL and Volleyball

The day following the end of the NFL regular season has come to be known as “Black Monday” as it is the day that head coaches of poorly performing teams are fired. I would suggest that some consideration be given to changing the term to “White Monday” because the firing of coaches has resulted primarily in the opening of head coaching positions to white coaches. On another coaching front, a similar story, but this one based on gender was highlight recently by The New York Times. Since the passage of Title IX, women’s sport has experienced considerable growth. At the NCAA Division I level, women playing volleyball outnumber men by a ratio of ten to one. At the recent finals of the NCAA Volleyball Championships, there were no women head coaches of the final four teams