Small Pseudo-Random Families of Matrices: Derandomizing Approximate Quantum Encryption

A quantum encryption scheme (also called private quantum channel, or state randomization protocol) is a one-time pad for quantum messages. If two parties share a classical random string, one of them can transmit a quantum state to the other so that an eavesdropper gets little or no information about the state being transmitted. Perfect encryption schemes leak no information at all about the message. Approximate encryption schemes leak a non-zero (though small) amount of information but require a shorter shared random key. Approximate schemes with short keys have been shown to have a number of applications in quantum cryptography and information theory. This paper provides the first deterministic, polynomial-time constructions of quantum approximate encryption schemes with short keys. Previous constructions (quant-ph/0307104) are probabilistic--that is, they show that if the operators used for encryption are chosen at random, then with high probability the resulting protocol will be a secure encryption scheme. Moreover, the resulting protocol descriptions are exponentially long. Our protocols use keys of the same length as (or better length than) the probabilistic constructions; to encrypt $n$ qubits approximately, one needs $n+o(n)$ bits of shared key. An additional contribution of this paper is a connection between classical combinatorial derandomization and constructions of pseudo-random matrix families in a continuous space.Comment: 11 pages, no figures. In Proceedings of RANDOM 2004, Cambridge, MA, August 200

Epsilon-Near-Zero Al-Doped ZnO for Ultrafast Switching at Telecom Wavelengths: Outpacing the Traditional Amplitude-Bandwidth Trade-Off

Transparent conducting oxides have recently gained great attention as CMOS-compatible materials for applications in nanophotonics due to their low optical loss, metal-like behavior, versatile/tailorable optical properties, and established fabrication procedures. In particular, aluminum doped zinc oxide (AZO) is very attractive because its dielectric permittivity can be engineered over a broad range in the near infrared and infrared. However, despite all these beneficial features, the slow (> 100 ps) electron-hole recombination time typical of these compounds still represents a fundamental limitation impeding ultrafast optical modulation. Here we report the first epsilon-near-zero AZO thin films which simultaneously exhibit ultra-fast carrier dynamics (excitation and recombination time below 1 ps) and an outstanding reflectance modulation up to 40% for very low pump fluence levels (< 4 mJ/cm2) at the telecom wavelength of 1.3 {\mu}m. The unique properties of the demonstrated AZO thin films are the result of a low temperature fabrication procedure promoting oxygen vacancies and an ultra-high carrier concentration. As a proof-of-concept, an all-optical AZO-based plasmonic modulator achieving 3 dB modulation in 7.5 {\mu}m and operating at THz frequencies is numerically demonstrated. Our results overcome the traditional "modulation depth vs. speed" trade-off by at least an order of magnitude, placing AZO among the most promising compounds for tunable/switchable nanophotonics.Comment: 14 pages, 9 figures, 1 tabl