From communication complexity to an entanglement spread area law in the ground state of gapped local Hamiltonians

In this work, we make a connection between two seemingly different problems. The first problem involves characterizing the properties of entanglement in the ground state of gapped local Hamiltonians, which is a central topic in quantum many-body physics. The second problem is on the quantum communication complexity of testing bipartite states with EPR assistance, a well-known question in quantum information theory. We construct a communication protocol for testing (or measuring) the ground state and use its communication complexity to reveal a new structural property for the ground state entanglement. This property, known as the entanglement spread, roughly measures the ratio between the largest and the smallest Schmidt coefficients across a cut in the ground state. Our main result shows that gapped ground states possess limited entanglement spread across any cut, exhibiting an "area law" behavior. Our result quite generally applies to any interaction graph with an improved bound for the special case of lattices. This entanglement spread area law includes interaction graphs constructed in [Aharonov et al., FOCS'14] that violate a generalized area law for the entanglement entropy. Our construction also provides evidence for a conjecture in physics by Li and Haldane on the entanglement spectrum of lattice Hamiltonians [Li and Haldane, PRL'08]. On the technical side, we use recent advances in Hamiltonian simulation algorithms along with quantum phase estimation to give a new construction for an approximate ground space projector (AGSP) over arbitrary interaction graphs.Comment: 29 pages, 1 figur

Adaptive Molecule Transmission Rate for Diffusion Based Molecular Communication

In this paper, a simple memory limited transmitter for molecular communication is proposed, in which information is encoded in the diffusion rate of the molecules. Taking advantage of memory, the proposed transmitter reduces the ISI problem by properly adjusting its diffusion rate. The error probability of the proposed scheme is derived and the result is compared with the lower bound on error probability of the optimum transmitter. It is shown that the performance of introduced transmitter is near optimal (under certain simplifications). Simplicity is the key feature of the presented communication system: the transmitter follows a simple rule, the receiver is a simple threshold decoder and only one type of molecule is used to convey the information

Cloning and Expression of Recombinant Nucleoprotein of Influenza H1N1

Background: Influenza virus is the major cause of lower respiratory tract illnesses on the worldwide. Vaccination can be an effective tool to prevent its outbreak. Highly conserved viral nucleoprotein is an effective vaccine candidate to provide heterosubtypic immunity, offering resistance against various influenza virus strains.Materials and Methods: In present research NP gene was inserted in pET-22b expression vector. New construct (pET-22b/NP) was transformed into E. coli BL21 (DE3) strain and the expression of nucleoprotein was induced by IPTG. It was analyzed by SDS-PAGE and confirmed by Western blotting.Results: Western blotting confirmed the expression and production of recombinant Influenza nucleoprotein.Conclusion: These results suggest that the codon-optimized influenza A virus NP gene can be efficiently expressed in E. coli

Efficiently Learning, Testing, and Simulating Quantum Many-Body Systems

This thesis focuses on quantum information and quantum computing, and their applications in studying quantum many-body systems. A remarkable interplay between computer science and quantum physics in the past few decades has revealed that a precise control and manipulation of interacting quantum systems enables us to process information and perform computations that go beyond the reach of conventional digital computers. This novel form of information processing has also resulted in a conceptually new toolkit for tackling fundamental questions about the physics of quantum many-body systems. This thesis studies new features of interacting quantum systems through the lens of computational complexity and information theory. We will see how using these new features in turn allows us to develop efficient classical and quantum algorithms for learning, testing, and simulating quantum many-body systems. Below are the main results of this thesis: 1. We develop an algorithm for reliably testing the amount of entanglement in a pure many-body quantum state. This algorithm tests whether a quantum state is a matrix product state of certain bond dimension in the property testing model. We provide both upper and lower bounds on the number of identical copies of the quantum state required by this algorithm. 2. We prove that a quantum information quantity, known as the entanglement spread, satisfies an area law in the ground state of any gapped local Hamiltonian with an arbitrary geometry. This new feature of ground-state entanglement is obtained using a connection to the seemingly different problem of finding the communication complexity of testing bipartite states. 3. We devise an algorithm for learning the local Hamiltonian that governs the interactions in a quantum many-body system. This algorithm uses the results of local measurements on the thermal state of the system, and provably only requires a number of samples that scales polynomially with the number of particles. 4. A quasi-polynomial time algorithm is developed that estimates the quantum partition function at temperatures above the phase transition point. We also study different characterizations of the thermal phase transition by connecting the exponential decay of correlations to the analyticity of the free energy in the high-temperature phase. 5. We rigorously bound the improvement that low-depth quantum circuits can provide over methods based on product states in estimating the ground-state energy of local Hamiltonians.Ph.D