ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 19 Nov 2019 12:54:34 GMT2019-11-19T12:54:34Z50101- Correlations in excited states of local Hamiltonianshttps://scholarbank.nus.edu.sg/handle/10635/116275Title: Correlations in excited states of local Hamiltonians
Authors: Chen, J.; Ji, Z.; Wei, Z.; Zeng, B.
Abstract: Physical properties of the ground and excited states of a k-local Hamiltonian are largely determined by the k-particle reduced density matrices (k-RDMs), or simply the k-matrix for fermionic systems-they are at least enough for the calculation of the ground-state and excited-state energies. Moreover, for a nondegenerate ground state of a k-local Hamiltonian, even the state itself is completely determined by its k-RDMs, and therefore contains no genuine k-particle correlations, as they can be inferred from k-particle correlation functions. It is natural to ask whether a similar result holds for nondegenerate excited states. In fact, for fermionic systems, it has been conjectured that any nondegenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any nondegenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure n-particle states. We construct explicit counterexamples to show that both conjectures are false. We further show that any nondegenerate excited state of a k-local Hamiltonian is a unique ground state of another 2k-local Hamiltonian, hence is uniquely determined by its 2k-RDMs (or 2k-matrix). These results set up a solid framework for the study of excited-state properties of many-body systems. © 2012 American Physical Society.
Mon, 09 Apr 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1162752012-04-09T00:00:00Z
- Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubitshttps://scholarbank.nus.edu.sg/handle/10635/112399Title: Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits
Authors: Ji, Z.; Wei, Z.; Zeng, B.
Abstract: The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground-state degeneracy is as hard as, but no harder than, its classical analog. © 2011 American Physical Society.
Thu, 27 Oct 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1123992011-10-27T00:00:00Z
- Experimental demonstration of quantum gain in a zero-sum gamehttps://scholarbank.nus.edu.sg/handle/10635/112434Title: Experimental demonstration of quantum gain in a zero-sum game
Authors: Zu, C.; Wang, Y.-X.; Chang, X.-Y.; Wei, Z.-H.; Zhang, S.-Y.; Duan, L.-M.
Abstract: We propose and experimentally demonstrate a zero-sum game that is in a fair Nash equilibrium for classical players, but has the property that a quantum player can always win using an appropriate strategy. The gain of the quantum player is measured experimentally for different quantum strategies and input states. It is found that the quantum gain is maximized by a maximally entangled state, but does not decrease to zero when entanglement disappears. Instead, it links with another kind of quantum correlation described by discord for the qubit case and the connection is demonstrated both theoretically and experimentally. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Thu, 01 Mar 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124342012-03-01T00:00:00Z
- Measurement-based quantum computing with valence-bond-solidshttps://scholarbank.nus.edu.sg/handle/10635/112568Title: Measurement-based quantum computing with valence-bond-solids
Authors: Kwek, L.C.; Wei, Z.; Zeng, B.
Abstract: Measurement-based quantum computing (MBQC) is a model of quantum computing that proceeds by sequential measurements of individual spins in an entangled resource state. However, it remains a challenge to produce efficiently such resource states. Would it be possible to generate these states by simply cooling a quantum many-body system to its ground state? Cluster states, the canonical resource states for MBQC, do not occur naturally as unique ground states of physical systems. This inherent hurdle has led to a significant effort to identify alternative resource states that appear as ground states in spin lattices. Recently, some interesting candidates have been identified with various valence-bond-solid (VBS) states. In this review, we provide a pedagogical introduction to recent progress regarding MBQC with VBS states as possible resource states. This study has led to an interesting interdisciplinary research area at the interface of quantum information science and condensed matter physics. © 2012 World Scientific Publishing Company.
Fri, 20 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1125682012-01-20T00:00:00Z
- Efficient protocols for generating bipartite classical distributions and quantum stateshttps://scholarbank.nus.edu.sg/handle/10635/77850Title: Efficient protocols for generating bipartite classical distributions and quantum states
Authors: Jain, R.; Shi, Y.; Wei, Z.; Zhang, S.
Abstract: We investigate the fundamental problem of generating bipartite classical distributions or quantum states. By designing efficient communication protocols and proving their optimality, we establish a number of intriguing connections to fundamental measures in optimization, convex geometry, and information theory. 1) To generate a classical distribution P(x,y) , we tightly characterize the minimum amount of quantum communication needed by the psd-rank of P (as a matrix), a measure recently proposed by Fiorini et al. (Proc. 44th ACM Symp. Theory Comput., pp. 95-106, 2012) in studies of the minimum size of extended formulations of optimization problems such as TSP. This echos the previous characterization for the optimal classical communication cost by the nonnegative rank of P. The result is obtained via investigating the more general case of bipartite quantum state generation and designing an optimal protocol for it. 2) When an approximation of is allowed to generate a distribution (X,Y)∼ P, we present a classical protocol of the communication cost O((C(X,Y)+1)) , where C(X,Y) is common information, a well-studied measure in information theory introduced by Wyner (IEEE Trans. Inf. Theory, 21 (2):163-179, 1975). This also links nonnegative rank and common information, two seemingly unrelated quantities in different fields. 3) For approximately generating a quantum pure state , we completely characterize the minimum cost by a corresponding approximate rank, closing a possibly exponential gap left in Ambainis et al. (SIAM J. Comput., 32 (6):1570-1585, 2003). © 2013 IEEE.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/778502013-01-01T00:00:00Z
- Quantum-capacity-approaching codes for the detected-jump channelhttps://scholarbank.nus.edu.sg/handle/10635/112509Title: Quantum-capacity-approaching codes for the detected-jump channel
Authors: Grassl, M.; Ji, Z.; Wei, Z.; Zeng, B.
Abstract: The quantum-channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known. Given the quantum capacity of a degradable channel, it remains challenging to find a practical coding scheme which approaches capacity. Here we discuss code designs for the detected-jump channel, a degradable channel with practical relevance describing the physics of spontaneous decay of atoms with detected photon emission. We show that this channel can be used to simulate a binary classical channel with both erasures and bit flips. The capacity of the simulated classical channel gives a lower bound on the quantum capacity of the detected-jump channel. When the jump probability is small, it almost equals the quantum capacity. Hence using a classical capacity-approaching code for the simulated classical channel yields a quantum code which approaches the quantum capacity of the detected-jump channel. © 2010 The American Physical Society.
Mon, 27 Dec 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1125092010-12-27T00:00:00Z
- Ground-state spaces of frustration-free Hamiltonianshttps://scholarbank.nus.edu.sg/handle/10635/116377Title: Ground-state spaces of frustration-free Hamiltonians
Authors: Chen, J.; Ji, Z.; Kribs, D.; Wei, Z.; Zeng, B.
Abstract: We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of "reduced spaces" to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set Θk of all the k-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in Θk, called atoms, are analogs of extreme points. We study the properties of atoms in Θk and discuss its relationship with ground states of k-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in Θ2 are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in Θk may not be the join of atoms, indicating a richer structure for Θk beyond the convex structure. Our study of Θk deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from the new perspective of reduced spaces. © 2012 American Institute of Physics.
Wed, 12 Sep 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1163772012-09-12T00:00:00Z
- Improving noise threshold for optical quantum computing with the EPR photon sourcehttps://scholarbank.nus.edu.sg/handle/10635/52987Title: Improving noise threshold for optical quantum computing with the EPR photon source
Authors: Wei, Z.-H.; Han, Y.-J.; Oh, C.H.; Duan, L.-M.
Abstract: We show that the noise threshold for optical quantum computing obtained by Varnava [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.100.060502 100, 060502 (2008)] can be significantly improved by replacing the single-photon source with the Einstein-Podolsky-Rosen (EPR) type of photon source. In this implementation, for an EPR source that emits either nothing (a vacuum state) or a perfect EPR state with probability ηs, the detector efficiency ηd is required to be larger than 50% and the source efficiency ηs can be an arbitrarily small positive number. We also present the error threshold for a more general noise model including additional photon absorption and show that the threshold still compares favorably with the previous results. We discuss several physical setups for realization of the required EPR photon source, including a photon emitter in a single-atom cavity. © 2010 The American Physical Society.
Fri, 11 Jun 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/529872010-06-11T00:00:00Z
- Full characterization of quantum correlated equilibriahttps://scholarbank.nus.edu.sg/handle/10635/112442Title: Full characterization of quantum correlated equilibria
Authors: Wei, Z.; Zhang, S.
Abstract: Quantum game theory aims to study interactions of people (or other agents) using quan- tum devices with possibly conflicting interests. Recently Zhang studied some quantita- tive questions in general quantum strategic games of growing sizes [19]. However, a fundamental question not addressed there is the characterization of quantum correlated equilibria (QCE). In this paper, we answer this question by giving a sufficient and nec- essary condition for an arbitrary state ρ being a QCE. In addition, when the condition fails to hold for some player i, we give an explicit positive-operator valued measurement (POVM) for that player to achieve a strictly positive gain of payoff. Finally, we give some upper bounds for the maximum gain by playing quantum strategies over classical ones, and the bounds are tight for some games. © Rinton Press.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124422013-01-01T00:00:00Z
- Efficient protocols for generating bipartite classical distributions and quantum stateshttps://scholarbank.nus.edu.sg/handle/10635/78120Title: Efficient protocols for generating bipartite classical distributions and quantum states
Authors: Jain, R.; Shi, Y.; Wei, Z.; Zhang, S.
Abstract: We investigate the fundamental problem of generating bipartite classical distributions or quantum states. By designing efficient communication protocols and proving their optimality, we establish a number of intriguing connections to fundamental measures in optimization, convex geometry, and information theory. 1. To generate a classical distribution P(x,y), we tightly characterize the minimum amount of quantum communication needed by the psd-rank of P (as a matrix), a measure recently proposed by Fiorini, Massar, Pokutta, Tiwary and de Wolf (Proceedings of the 44th ACM Symposium on Theory of Computing, pages 95-106, 2012) in studies of the minimum size of extended formulations of optimization problems such as TSP. This echos the previous characterization for the optimal classical communication cost by the nonnegative rank of P. The result is obtained via investigating the more general case of bipartite quantum state generation and designing an optimal protocol for it. 2. When an approximation of ε is allowed to generate a distribution (X, Y) ∼ P, we present a classical protocol of the communication cost O((C(X, Y) + 1)/ε), where C(X, Y) is common information, a well-studied measure in information theory introduced by Wyner (IEEE Transactions on Information Theory, 21(2):163-179, 1975). This also links nonnegative rank and common information, two seemingly unrelated quantities in different fields. 3. For approximately generating a quantum pure state |ψ〉, we completely characterize the minimum cost by a corresponding approximate rank, closing a possibly exponential gap left in Ambainis, Schulman, Ta-Shma, Vazirani and Wigderson. Copyright © SIAM.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/781202013-01-01T00:00:00Z