Quantum error correction may delay, but also cause, entanglement sudden death

Dissipation may cause two initially entangled qubits to evolve into a separable state in a finite time. This behavior is called entanglement sudden death (ESD). We study to what extent quantum error correction can combat ESD. We find that in some cases quantum error correction can delay entanglement sudden death but in other cases quantum error correction may cause ESD for states that otherwise do not suffer from it. Our analysis also shows that fidelity may not be the best measure to compare the efficiency of different error correction codes since the fidelity is not directly coupled to a state's remaining entanglement.Comment: 3 figure

Entanglement invariant for the double Jaynes-Cummings model

We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings hamiltonians, via the entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as "entanglement sudden death". We find a natural entanglement invariant under evolution demonstrating that entanglement sudden death is caused by ignoring (tracing over) some of the system's degrees of freedom that become entangled through the interaction.Comment: Sec. V has largely been rewritten. An error pertaining to the entanglement invariant has been corrected and a correct invariant valid for a much larger set of states have been found, Eq. (25

Tunable effective g-factor in InAs nanowire quantum dots

We report tunneling spectroscopy measurements of the Zeeman spin splitting in InAs few-electron quantum dots. The dots are formed between two InP barriers in InAs nanowires with a wurtzite crystal structure grown by chemical beam epitaxy. The values of the electron g-factors of the first few electrons entering the dot are found to strongly depend on dot size and range from close to the InAs bulk value in large dots |g^*|=13 down to |g^*|=2.3 for the smallest dots. These findings are discussed in view of a simple model.Comment: 4 pages, 3 figure

Imaging a 1-electron InAs quantum dot in an InAs/InP nanowire

Nanowire heterostructures define high-quality few-electron quantum dots for nanoelectronics, spintronics and quantum information processing. We use a cooled scanning probe microscope (SPM) to image and control an InAs quantum dot in an InAs/InP nanowire, using the tip as a movable gate. Images of dot conductance vs. tip position at T = 4.2 K show concentric rings as electrons are added, starting with the first electron. The SPM can locate a dot along a nanowire and individually tune its charge, abilities that will be very useful for the control of coupled nanowire dots

Two-photon imaging and quantum holography

It has been claimed that ``the use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever strength of the correlations between the two photons'' [A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001)]. While we believe that the cited statement is true, we show that the method proposed in that paper, with ``bucket detection'' of one of the photons, will give identical results for entangled states as for appropriately prepared classically correlated states.Comment: 4 pages, 2 figures, REVTe

Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio

We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price options on non-traded assets for which there is a traded asset that is correlated to the non-traded asset. Our main contribution to this particular problem is to show that our seller/buyer prices are the upper/lower good deal bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko (2006) and to determine the analytical properties of these prices. Second, we apply our method to price options in the presence of stochastic volatility. Our main contribution to this problem is to show that the instantaneous Sharpe ratio, an integral ingredient in our methodology, is the negative of the market price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar (2000).Comment: Keywords: Pricing derivative securities, incomplete markets, Sharpe ratio, correlated assets, stochastic volatility, non-linear partial differential equations, good deal bound

Certainty relations between local and nonlocal observables

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.Comment: 4 pages, no figure

Entangled-State Lithography: Tailoring any Pattern with a Single State

We demonstrate a systematic approach to Heisenberg-limited lithographic image formation using four-mode reciprocal binominal states. By controlling the exposure pattern with a simple bank of birefringent plates, any pixel pattern on a $(N+1) \times (N+1)$ grid, occupying a square with the side half a wavelength long, can be generated from a $2 N$-photon state.Comment: 4 pages, 4 figure

GaAs Nanowire pn-Junctions Produced by Low-Cost and High-Throughput Aerotaxy

Semiconductor nanowires could significantly boost the functionality and performance of future electronics, light-emitting diodes, and solar cells. However, realizing this potential requires growth methods that enable high-throughput and low-cost production of nanowires with controlled doping. Aerotaxy is an aerosol-based method with extremely high growth rate that does not require a growth substrate, allowing mass-production of high-quality nanowires at a low cost. So far, pn-junctions, a crucial element of solar cells and light-emitting diodes, have not been realized by Aerotaxy growth. Here we report a further development of the Aerotaxy method and demonstrate the growth of GaAs nanowire pn-junctions. Our Aerotaxy system uses an aerosol generator for producing the catalytic seed particles, together with a growth reactor with multiple consecutive chambers for growth of material with different dopants. We show that the produced nanowire pn-junctions have excellent diode characteristics with a rectification ratio of >105, an ideality factor around 2, and very promising photoresponse. Using electron beam induced current and hyperspectral cathodoluminescence, we determined the location of the pn-junction and show that the grown nanowires have high doping levels, as well as electrical properties and diffusion lengths comparable to nanowires grown using metal organic vapor phase epitaxy. Our findings demonstrate that high-quality GaAs nanowire pn-junctions can be produced using a low-cost technique suitable for mass-production, paving the way for industrial-scale production of nanowire-based solar cells