A holographic proof of the strong subadditivity of entanglement entropy

When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as "strong subadditivity". For a field theory this inequality can be stated as follows: given any two regions of space $A$ and $B$, $S(A) + S(B) \ge S(A \cup B) + S(A \cap B)$. Recently, a method has been found for computing entanglement entropies in any field theory for which there is a holographically dual gravity theory. In this note we give a simple geometrical proof of strong subadditivity employing this holographic prescription.Comment: 9 pages, 3 figure

Thermal entanglement in the nanotubular system Na_2V_3O_7

Macroscopic entanglement witnesses have been put forward recently to reveal nonlocal quantum correlations between individual constituents of the solid at nonzero temperatures. Here we apply a recently proposed universal entanglement witness, the magnetic susceptibility [New J. Phys. {\bf 7}, 258 (2005)] for the estimation of the critical temperature $T_c$ in the nanotubular system ${\rm Na_2V_3O_7}$ below which thermal entanglement is present. As a result of an analysis based on the experimental data for dc-magnetic susceptibility, we show that $T_c \approx 365$ K, which is approximately three times higher than the critical temperature corresponding to the bipartite entanglement.Comment: 6 pages, 3 figures, REVTeX

Analysis of a convenient information bound for general quantum channels

Open questions from Sarovar and Milburn (2006 J.Phys. A: Math. Gen. 39 8487) are answered. Sarovar and Milburn derived a convenient upper bound for the Fisher information of a one-parameter quantum channel. They showed that for quasi-classical models their bound is achievable and they gave a necessary and sufficient condition for positive operator-valued measures (POVMs) attaining this bound. They asked (i) whether their bound is attainable more generally, (ii) whether explicit expressions for optimal POVMs can be derived from the attainability condition. We show that the symmetric logarithmic derivative (SLD) quantum information is less than or equal to the SM bound, i.e.\ $H(\theta) \leq C_{\Upsilon}(\theta)$ and we find conditions for equality. As the Fisher information is less than or equal to the SLD quantum information, i.e. $F_M(\theta) \leq H(\theta)$, we can deduce when equality holds in $F_M(\theta) \leq C_{\Upsilon}(\theta)$. Equality does not hold for all channels. As a consequence, the attainability condition cannot be used to test for optimal POVMs for all channels. These results are extended to multi-parameter channels.Comment: 16 pages. Published version. Some of the lemmas have been corrected. New resuts have been added. Proofs are more rigorou

Overcoming a limitation of deterministic dense coding with a non-maximally entangled initial state

Under two-party deterministic dense-coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |Psi>. If |Psi> represents a maximally entangled state (i.e., each of its Schmidt coefficients is sqrt(1/d)), then Alice can convey to Bob one of d^2 distinct messages. If |Psi> is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice's qudit, it is impossible to encode d^2-1 messages. Encoding d^2-2 is possible; see, e.g., the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when |Psi> is not maximally entangled, the communications limit of d^2-2 messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of |Psi> is sufficiently close to sqrt(1/d). In this protocol, d^2-2 of the messages are encoded via unitary operations on Alice's qudit, and the final (d^2-1)-th message is encoded via a (non-trace-preserving) quantum operation.Comment: 18 pages, published versio

Hydrogenic Spin Quantum Computing in Silicon: A Digital Approach

We suggest an architecture for quantum computing with spin-pair encoded qubits in silicon. Electron-nuclear spin-pairs are controlled by a dc magnetic field and electrode-switched on and off hyperfine interaction. This digital processing is insensitive to tuning errors and easy to model. Electron shuttling between donors enables multi-qubit logic. These hydrogenic spin qubits are transferable to nuclear spin-pairs, which have long coherence times, and electron spin-pairs, which are ideally suited for measurement and initialization. The architecture is scalable to highly parallel operation.Comment: 4 pages, 5 figures; refereed and published version with improved introductio

High purity bright single photon source

Using cavity-enhanced non-degenerate parametric downconversion, we have built a frequency tunable source of heralded single photons with a narrow bandwidth of 8 MHz, making it compatible with atomic quantum memories. The photon state is 70% pure single photon as characterized by a tomographic measurement and reconstruction of the quantum state, revealing a clearly negative Wigner function. Furthermore, it has a spectral brightness of ~1,500 photons/s per MHz bandwidth, making it one of the brightest single photon sources available. We also investigate the correlation function of the down-converted fields using a combination of two very distinct detection methods; photon counting and homodyne measurement.Comment: 9 pages, 4 figures; minor changes, added referenc

Natural selection reduced diversity on human Y chromosomes

The human Y chromosome exhibits surprisingly low levels of genetic diversity. This could result from neutral processes if the effective population size of males is reduced relative to females due to a higher variance in the number of offspring from males than from females. Alternatively, selection acting on new mutations, and affecting linked neutral sites, could reduce variability on the Y chromosome. Here, using genome-wide analyses of X, Y, autosomal and mitochondrial DNA, in combination with extensive population genetic simulations, we show that low observed Y chromosome variability is not consistent with a purely neutral model. Instead, we show that models of purifying selection are consistent with observed Y diversity. Further, the number of sites estimated to be under purifying selection greatly exceeds the number of Y-linked coding sites, suggesting the importance of the highly repetitive ampliconic regions. While we show that purifying selection removing deleterious mutations can explain the low diversity on the Y chromosome, we cannot exclude the possibility that positive selection acting on beneficial mutations could have also reduced diversity in linked neutral regions, and may have contributed to lowering human Y chromosome diversity. Because the functional significance of the ampliconic regions is poorly understood, our findings should motivate future research in this area.Comment: 43 pages, 11 figure