The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings

Valiant-Vazirani showed in 1985 that solving NP with the promise that "yes" instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions). We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur (MA) and Quantum-Classical-Merlin-Arthur (QCMA). Our results have implications on the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation, to within polynomial accuracy, of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized reductions. This is in strong contrast to the case of constant gapped 1-D Hamiltonians, which is in NP. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian which allows the calculation of expectation values efficiently. Finally, we discuss a few obstacles towards establishing an analogous result to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random projections fail to provide a polynomial gap between two witnesses

Universally Composable Quantum Multi-Party Computation

The Universal Composability model (UC) by Canetti (FOCS 2001) allows for secure composition of arbitrary protocols. We present a quantum version of the UC model which enjoys the same compositionality guarantees. We prove that in this model statistically secure oblivious transfer protocols can be constructed from commitments. Furthermore, we show that every statistically classically UC secure protocol is also statistically quantum UC secure. Such implications are not known for other quantum security definitions. As a corollary, we get that quantum UC secure protocols for general multi-party computation can be constructed from commitments

Reduction of Soil-Borne Plant Pathogens Using Lime and Ammonia Evolved from Broiler Litter

In laboratory and micro-plots simulations and in a commercial greenhouse, soil ammonia (NH3) and pH were manipulated as means to control soil-borne fungal pathogens and nematodes. Soil ammonification capacity was increased by applying low C/N ratio broiler litter at 1–8% (w/w). Soil pH was increased using lime at 0.5–1% (w/w). This reduced fungi (Fusarium oxysporum f. sp. dianthi and Sclerotium rolfsii) and root-knot nematode (Meloidogyne javanica) in lab tests below detection. In a commercial greenhouse, broiler litter (25 Mg ha−1) and lime (12.5 Mg ha−1) addition to soil in combination with solarization significantly reduced M. javanica induced root galling of tomato test plants from 47% in the control plots (solarization only) to 7% in treated plots. Root galling index of pepper plants, measured 178 days after planting in the treated and control plots, were 0.8 and 1.5, respectively, which was statistically significantly different. However, the numbers of nematode juveniles in the root zone soil counted 83 and 127 days after pepper planting were not significantly different between treatments. Pepper fruit yield was not different between treatments. Soil disinfection and curing was completed within one month, and by the time of bell-pepper planting the pH and ammonia values were normal

The impact of vector resonant relaxation on the evolution of binaries near a massive black hole: implications for gravitational wave sources

Binaries within the sphere of influence of a massive black hole (MBH) in galactic nuclei are susceptible to the Lidov-Kozai (LK) mechanism, which can drive orbits to high eccentricities and trigger strong interactions within the binary such as the emission of gravitational waves (GWs), and mergers of compact objects. These events are potential sources for GW detectors such as Advanced LIGO and VIRGO. The LK mechanism is only effective if the binary is highly inclined with respect to its orbit around the MBH (within a few degrees of 90 deg), implying low rates. However, close to an MBH, torques from the stellar cluster give rise to the process of vector resonant relaxation (VRR). VRR can bring a low-inclination binary into an `active' LK regime in which high eccentricities and strong interactions are triggered in the binary. Here, we study the coupled LK-VRR dynamics, with implications for LIGO and VIRGO GW sources. We carry out Monte Carlo simulations and find that the merger fraction enhancement due to LK-VRR dynamics is up to a factor of ~10 for the lower end of assumed MBH masses (M_MBH = 1e4 MSun), and decreases sharply with increasing M_MBH. We find that, even in our most optimistic scenario, the baseline BH-BH merger rate is small, and the enhancement by LK-VRR coupling is not large enough to increase the rate to well above the LIGO/VIRGO lower limit, 12 Gpc^{-3} yr^{-1}. For the Galactic Center, the LK-VRR-enhanced rate is ~100 times lower than the LIGO/VIRGO limit, and for M_MBH = 1e4 MSun, the rate barely reaches 12 Gpc^{-3} yr^{-1}.Comment: Accepted for publication in ApJ. 22 pages, 20 figure

The quantum one-time pad in the presence of an eavesdropper

A classical one-time pad allows two parties to send private messages over a public classical channel -- an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single letter formula for the rate at which the two parties can send messages using a quantum one-time pad

Locking of accessible information and implications for the security of quantum cryptography

The unconditional security of a quantum key distribution protocol is often defined in terms of the accessible information, that is, the maximum mutual information between the distributed key S and the outcome of an optimal measurement on the adversary's (quantum) system. We show that, even if this quantity is small, certain parts of the key S might still be completely insecure when S is used in applications, such as for one-time pad encryption. This flaw is due to a locking property of the accessible information: one additional (physical) bit of information might increase the accessible information by more than one bit.Comment: 5 pages; minor change

The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings

Valiant-Vazirani showed in 1985 that solving NP with the promise that "yes" instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions). We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur (MA) and Quantum-Classical-Merlin-Arthur (QCMA). Our results have implications on the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation, to within polynomial accuracy, of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized reductions. This is in strong contrast to the case of constant gapped 1-D Hamiltonians, which is in NP. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian which allows the calculation of expectation values efficiently. Finally, we discuss a few obstacles towards establishing an analogous result to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random projections fail to provide a polynomial gap between two witnesses

Security of practical private randomness generation

Measurements on entangled quantum systems necessarily yield outcomes that are intrinsically unpredictable if they violate a Bell inequality. This property can be used to generate certified randomness in a device-independent way, i.e., without making detailed assumptions about the internal working of the quantum devices used to generate the random numbers. Furthermore these numbers are also private, i.e., they appear random not only to the user, but also to any adversary that might possess a perfect description of the devices. Since this process requires a small initial random seed, one usually speaks of device-independent randomness expansion. The purpose of this paper is twofold. First, we point out that in most real, practical situations, where the concept of device-independence is used as a protection against unintentional flaws or failures of the quantum apparatuses, it is sufficient to show that the generated string is random with respect to an adversary that holds only classical-side information, i.e., proving randomness against quantum-side information is not necessary. Furthermore, the initial random seed does not need to be private with respect to the adversary, provided that it is generated in a way that is independent from the measured systems. The devices, though, will generate cryptographically-secure randomness that cannot be predicted by the adversary and thus one can, given access to free public randomness, talk about private randomness generation. The theoretical tools to quantify the generated randomness according to these criteria were already introduced in [S. Pironio et al, Nature 464, 1021 (2010)], but the final results were improperly formulated. The second aim of this paper is to correct this inaccurate formulation and therefore lay out a precise theoretical framework for practical device-independent randomness expansion.Comment: 18 pages. v3: important changes: the present version focuses on security against classical side-information and a discussion about the significance of these results has been added. v4: minor changes. v5: small typos correcte

High-dimensional coherent one-way quantum key distribution

High-dimensional quantum key distribution (QKD) offers secure communication, with secure key rates that surpass those achievable by QKD protocols utilizing two-dimensional encoding. However, existing high-dimensional QKD protocols require additional experimental resources, such as multiport interferometers and multiple detectors, thus raising the cost of practical high-dimensional systems and limiting their use. Here, we present and analyze a novel protocol for arbitrary-dimensional QKD, that requires only the hardware of a standard two-dimensional system. We provide security proofs against individual attacks and coherent attacks, setting an upper and lower bound on the secure key rates. Then, we test the new high-dimensional protocol in a standard two-dimensional QKD system over a 40 km fiber link. The new protocol yields a two-fold enhancement of the secure key rate compared to the standard two-dimensional coherent one-way protocol, without introducing any hardware modifications to the system. This work, therefore, holds great potential to enhance the performance of already deployed time-bin QKD systems through a software update alone. Furthermore, its applications extend across different encoding schemes of QKD qudits