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Vwani Roychowdhury

Publications and source records attributed to Vwani Roychowdhury.

At least 55 records · Page 3Linked to original sources

Robustness of entangled states that are positive under partial transposition

We study robustness of bipartite entangled states that are positive under partial transposition (PPT). It is shown that almost all PPT entangled states are unconditionally robust, in the sense, both inseparability and positivity are preserved under sufficiently small perturbations in its immediate neighborhood. Such unconditionally robust PPT entangled states lie inside an open PPT entangled ball. We construct examples of such balls whose radii are shown to be finite and can be explicitly calculated. This provides a lower bound on the volume of all PPT entangled states. Multipartite generalization of our constructions are also outlined.

quant-ph↗

Boundary effects to the entanglement entropy and two-site entanglement of the spin-1 valence-bond solid

We investigate the von Neumann entropy of a block of subsystem for the valence-bond solid (VBS) state with general open boundary conditions. We show that the effect of the boundary on the von Neumann entropy decays exponentially fast in the distance between the subsystem considered and the boundary sites. Further, we show that as the size of the subsystem increases, its von Neumann entropy exponentially approaches the summation of the von Neumann entropies of the two ends, the exponent being related to the size. In contrast to critical systems, where boundary effects to the von Neumann entropy decay slowly, the boundary effects in a VBS, a non-critical system, decay very quickly. We also study the entanglement between two spins. Curiously, while the boundary operators decrease the von Neumann entropy of L spins, they increase the entanglement between two spins.

quant-ph↗

Entangled multi-qubit states without higher-tangle

We analyze mixed multi-qubit states composed of a W class state and a product state with all qubit in |0>. We find the optimal pure state decomposition and convex roofs for higher-tangle with bipartite partition between one qubit and the rest qubits for those mixed states. The optimality of the decomposition is ensured by the Coffman-Kundu-Wootters (CKW) inequality which describes the monogamy of quantum entanglement. The generalized monogamy inequality is found to be true for W class states with arbitrary partitions between one qubit and multi-qubit.

quant-ph↗

Superadditivity of distillable entanglement From Quantum Teleportation

We show that the phenomenon of superadditivity of distillable entanglement observed in multipartite quantum systems results from the consideration of states created during the execution of the standard end-to-end quantum teleportation protocol (and a few additional local operations and classical communication (LOCC) steps) on a linear chain of singlets. Some of these intermediate states are tensor products of bound-entangled (BE) states, and hence, by construction possess distillable entanglement, which can be unlocked by simply completing the rest of the LOCC operations required by the underlying teleportation protocol. We use this systematic approach to construct both new and known examples of superactivation of bound entanglement, and first examples of activation of BE states using other BE states. A surprising outcome is the construction of noiseless quantum relay channels with no distillable entanglement between any two parties, except for that between the two end nodes.

quant-ph↗

Valence-Bond-Solid state entanglement in a 2-D Cayley tree

The Valence-Bond-Solid (VBS) states are in general ground states for certain gapped models. We consider the entanglement of VBS states on a two-dimensional Cayley tree. We show that the entropy of the reduced density operator does not depend on the whole size of the Cayley tree. We also show that asymptotically, the entropy is liearly proportional to the number of singlet states cut by the reduced density operator of the VBS state.

quant-ph↗

A Proof of the Security of Quantum Key Distribution

We prove the security of theoretical quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages such that their security is also unaffected in the future.

quant-ph↗

Eigenvalue Estimation of Differential Operators

We demonstrate how linear differential operators could be emulated by a quantum processor, should one ever be built, using the Abrams-Lloyd algorithm. Given a linear differential operator of order 2S, acting on functions psi(x_1,x_2,...,x_D) with D arguments, the computational cost required to estimate a low order eigenvalue to accuracy Theta(1/N^2) is Theta((2(S+1)(1+1/nu)+D)log N) qubits and O(N^{2(S+1)(1+1/nu)} (D log N)^c) gate operations, where N is the number of points to which each argument is discretized, nu and c are implementation dependent constants of O(1). Optimal classical methods require Theta(N^D) bits and Omega(N^D) gate operations to perform the same eigenvalue estimation. The Abrams-Lloyd algorithm thereby leads to exponential reduction in memory and polynomial reduction in gate operations, provided the domain has sufficiently large dimension D > 2(S+1)(1+1/nu). In the case of Schrodinger's equation, ground state energy estimation of two or more particles can in principle be performed with fewer quantum mechanical gates than classical gates.

quant-ph↗

Optimal two-qubit quantum circuits using exchange interactions

The Heisenberg exchange interaction is a natural method to implement non-local (i.e., multi-qubit) quantum gates in quantum information processing. We consider quantum circuits comprising of $(SWAP)^α$ gates, which are realized through the exchange interaction, and single-qubit gates. A universal two-qubit quantum circuit is constructed from only three $(SWAP)^α$ gates and six single-qubit gates. We further show that three $(SWAP)^α$ gates are not only sufficient, but necessary. Since six single-qubit gates are known to be necessary, our universal two-qubit circuit is optimal in terms of the number of {\em both} $(SWAP)^α$ and single-qubit gates.

quant-ph↗

Multiple Scale-Free Structures in Complex Ad-Hoc Networks

This paper develops a framework for analyzing and designing dynamic networks comprising different classes of nodes that coexist and interact in one shared environment. We consider {\em ad hoc} (i.e., nodes can leave the network unannounced, and no node has any global knowledge about the class identities of other nodes) {\em preferentially grown networks}, where different classes of nodes are characterized by different sets of local parameters used in the stochastic dynamics that all nodes in the network execute. We show that multiple scale-free structures, one within each class of nodes, and with tunable power-law exponents (as determined by the sets of parameters characterizing each class) emerge naturally in our model. Moreover, the coexistence of the scale-free structures of the different classes of nodes can be captured by succinct phase diagrams, which show a rich set of structures, including stable regions where different classes coexist in heavy-tailed and light-tailed states, and sharp phase transitions. Finally, we show how the dynamics formulated in this paper will serve as an essential part of {\em ad-hoc networking protocols}, which can lead to the formation of robust and efficiently searchable networks (including, the well-known Peer-To-Peer (P2P) networks) even under very dynamic conditions.

cond-mat.dis-nn↗

Non-full rank bound entangled states satisfying the range criterion

A systematic method for generating bound entangled states in any bipartite system, with ranks ranging from five to full rank, is presented. These states are constructed by mixing separable states with UPB (Unextendible Product Basis) - generated PPT bound entangled states. A subset of this class of PPT bound entangled states, having less than full rank, is shown to satisfy the range criterion [Phys. Lett. A, vol. 232 (1997) 333].

quant-ph↗

Entanglement in a Valence-Bond-Solid State

We study entanglement in Valence-Bond-Solid state. It describes the ground state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model has a gap and open boundary conditions. We calculate an entropy of a subsystem (continuous block of spins). It quantifies the entanglement of this block with the rest of the ground state. We prove that the entanglement approaches a constant value exponentially fast as the size of the subsystem increases. Actually we proved that the density matrix of the continuous block of spins depends only on the length of the block, but not on the total size of the chain [distance to the ends also not essential]. We also study reduced density matrices of two spins both in the bulk and on the boundary. We evaluated concurrencies.

quant-ph↗

Maximally-Disordered Distillable Quantum States

We explore classical to quantum transition of correlations by studying the quantum states located just outside of the classically-correlated-states-only neighborhood of the maximally mixed state (the largest separable ball (LSB)). We show that a natural candidate for such states raises the possibility of a layered transition, i.e., an annular region comprising only classical and the classical-like bound entangled states, followed by free or distillable entanglement. Surprisingly, we find the transition to be abrupt for bipartite systems: distillable states emerge arbitrarily close to the LSB. For multipartite systems, while the radius of the LSB remains unknown, we determine the radius of the largest undistillable ball. Our results also provide an upper bound on how noisy shared entangled states can be for executing quantum information processing protocols.

quant-ph↗

Personal Email Networks: An Effective Anti-Spam Tool

We provide an automated graph theoretic method for identifying individual users' trusted networks of friends in cyberspace. We routinely use our social networks to judge the trustworthiness of outsiders, i.e., to decide where to buy our next car, or to find a good mechanic for it. In this work, we show that an email user may similarly use his email network, constructed solely from sender and recipient information available in the email headers, to distinguish between unsolicited commercial emails, commonly called "spam", and emails associated with his circles of friends. We exploit the properties of social networks to construct an automated anti-spam tool which processes an individual user's personal email network to simultaneously identify the user's core trusted networks of friends, as well as subnetworks generated by spams. In our empirical studies of individual mail boxes, our algorithm classified approximately 53% of all emails as spam or non-spam, with 100% accuracy. Some of the emails are left unclassified by this network analysis tool. However, one can exploit two of the following useful features. First, it requires no user intervention or supervised training; second, it results in no false negatives i.e., spam being misclassified as non-spam, or vice versa. We demonstrate that these two features suggest that our algorithm may be used as a platform for a comprehensive solution to the spam problem when used in concert with more sophisticated, but more cumbersome, content-based filters.

cond-mat.dis-nn↗

Algorithmic Cooling of Spins: A Practicable Method for Increasing Polarization

An efficient technique to generate ensembles of spins that are highly polarized by external magnetic fields is the Holy Grail in Nuclear Magnetic Resonance (NMR) spectroscopy. Since spin-half nuclei have steady-state polarization biases that increase inversely with temperature, spins exhibiting high polarization biases are considered cool, even when their environment is warm. Existing spin-cooling techniques are highly limited in their efficiency and usefulness. Algorithmic cooling is a promising new spin-cooling approach that employs data compression methods in open systems. It reduces the entropy of spins on long molecules to a point far beyond Shannon's bound on reversible entropy manipulations (an information-theoretic version of the 2nd Law of Thermodynamics), thus increasing their polarization. Here we present an efficient and experimentally feasible algorithmic cooling technique that cools spins to very low temperatures even on short molecules. This practicable algorithmic cooling could lead to breakthroughs in high-sensitivity NMR spectroscopy in the near future, and to the development of scalable NMR quantum computers in the far future. Moreover, while the cooling algorithm itself is classical, it uses quantum gates in its implementation, thus representing the first short-term application of quantum computing devices.

quant-ph↗

Scale-Free and Stable Structures in Complex {\em Ad hoc} networks

Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and random deletions of existing nodes (and, hence, the associated links). We first show that dynamics based {\em only} on the well-known preferential attachments of new nodes {\em do not} lead to a sufficiently heavy-tailed degree distribution in {\em ad hoc} networks. In particular, the magnitude of the power-law exponent increases rapidly (from 3) with the deletion rate, becoming $\infty$ in the limit of equal insertion and deletion rates. \iffalse ; thus, forcing the degree distribution to be essentially an exponential one.\fi We then introduce a {\em local} and {\em universal} {\em compensatory rewiring} dynamic, and show that even in the limit of equal insertion and deletion rates true scale-free structures emerge, where the degree distributions obey a power-law with a tunable exponent, which can be made arbitrarily close to -2. These results provide the first-known evidence of emergence of scale-free degree distributions purely due to dynamics, i.e., in networks of almost constant average size. The dynamics discovered in this paper can be used to craft protocols for designing highly dynamic Peer-to-Peer networks, and also to account for the power-law exponents observed in existing popular services.

cond-mat.dis-nn↗

New classes of n-copy undistillable quantum states with negative partial transposition

The discovery of entangled quantum states from which one cannot distill pure entanglement constitutes a fundamental recent advance in the field of quantum information. Such bipartite bound-entangled (BE) quantum states \emph{could} fall into two distinct categories: (1) Inseparable states with positive partial transposition (PPT), and (2) States with negative partial transposition (NPT). While the existence of PPT BE states has been confirmed, \emph{only one} class of \emph{conjectured} NPT BE states has been discovered so far. We provide explicit constructions of a variety of multi-copy undistillable NPT states, and conjecture that they constitute families of NPT BE states. For example, we show that for every pure state of Schmidt rank greater than or equal to three, one can construct n-copy undistillable NPT states, for any $n\geq1$. The abundance of such conjectured NPT BE states, we believe, considerably strengthens the notion that being NPT is only a necessary condition for a state to be distillable.

quant-ph↗

A Random Structure for Optimum Cache Size Distributed hash table (DHT) Peer-to-Peer design

We propose a new and easily-realizable distributed hash table (DHT) peer-to-peer structure, incorporating a random caching strategy that allows for {\em polylogarithmic search time} while having only a {\em constant cache} size. We also show that a very large class of deterministic caching strategies, which covers almost all previously proposed DHT systems, can not achieve polylog search time with constant cache size. In general, the new scheme is the first known DHT structure with the following highly-desired properties: (a) Random caching strategy with constant cache size; (b) Average search time of $O(log^{2}(N))$; (c) Guaranteed search time of $O(log^{3}(N))$; (d) Truly local cache dynamics with constant overhead for node deletions and additions; (e) Self-organization from any initial network state towards the desired structure; and (f) Allows a seamless means for various trade-offs, e.g., search speed or anonymity at the expense of larger cache size.

cs.NI↗

Partial recovery of entanglement in bipartite entanglement transformations

Any deterministic bipartite entanglement transformation involving finite copies of pure states and carried out using local operations and classical communication (LOCC) results in a net loss of entanglement. We show that for almost all such transformations, partial recovery of lost entanglement is achievable by using $2 \times 2$ auxiliary entangled states, no matter how large the dimensions of the parent states are. For the rest of the special cases of deterministic LOCC transformations, we show that the dimension of the auxiliary entangled state depends on the presence of equalities in the majorization relations of the parent states. We show that genuine recovery is still possible using auxiliary states in dimensions less than that of the parent states for all patterns of majorization relations except only one special case.

quant-ph↗