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D. M. Tong

Publications and source records attributed to D. M. Tong.

At least 55 records · Page 3Linked to original sources
arXiv2014

Completely positive maps within the framework of direct-sum decomposition of state space

We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They includes not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.

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arXiv2014

Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies

Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In this paper, we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on non-adiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.

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arXiv2014

Coexistence of Kochen-Specker inequalities and noncontextuality inequalities

Two types of inequalities, Kochen-Specker inequalities and noncontextuality inequalities, are both used to demonstrate the incompatibility between the noncontextual hidden variable model and quantum mechanics. It has been thought that noncontextuality inequalities are much more potent than Kochen-Specker inequalities, since the latter are constrained by the Kochen-Specker rules, which are regarded as an extra constraint imposed on the noncontextual hidden variable model. However, we find that a noncontextuality inequality exists in a ray set if and only if a Kochen-Specker inequality exists in the same ray set. This provides an effect approach both for constructing noncontextuality inequalities in a Kochen-Specker set and for converting a Kochen-Specker inequality to a noncontextuality inequality in any ray set.

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arXiv2013

Robustness of non-adiabatic holonomic gates

The robustness to different sources of error of the scheme for non-adiabatic holonomic gates proposed in [New J. Phys. {\bf 14}, 103035 (2012)] is investigated. Open system effects as well as errors in the driving fields are considered. It is found that the gates can be made error resilient by using sufficiently short pulses. The principal limit of how short the pulses can be made is given by the breakdown of the quasi-monochromatic approximation. A comparison with the resilience of adiabatic gates is carried out.

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arXiv2012

Non-adiabatic holonomic quantum computation

We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $Λ$ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.

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arXiv2012

Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, non-adiabatic holonomic quantum computation in decoherence-free subspaces, which avoids long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize non-adiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

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arXiv2010

Separable states and the geometric phases of an interacting two-spin system

It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. In this paper, we illustrate this point by investigating a well known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.

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arXiv2009

Geometric phase of a quantum dot system in nonunitary evolution

Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent control of single electron have suggested that electron in quantum dot systems is a promising candidate of qubit in future quantum information processing devices. In this paper, by considering a feasible quantum dot model, we calculate the geometric phase of the quantum dot system in nonunitary evolution and investigate the effect of environment parameters on the phase value.

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arXiv2006

Effective Hamiltonian approach to adiabatic approximation in open systems

The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic evolution of the open system is then defined as the adiabatic dynamics of the composite system. Validity and invalidity conditions for this approximation are established and discussed. A High-order adiabatic approximation for open systems is introduced. As an example, the adiabatic condition for an open spin-$\frac 1 2$ particle in time-dependent magnetic fields is analyzed.

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arXiv2006

Quantitative conditions do not guarantee the validity of the adiabatic approximation

In this letter, we point out that the widely used quantitative conditions in the adiabatic theorem are insufficient in that they do not guarantee the validity of the adiabatic approximation. We also reexamine the inconsistency issue raised by Marzlin and Sanders (Phys. Rev. Lett. 93, 160408, 2004) and elucidate the underlying cause.

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arXiv2006

Geometric phase in open systems: beyond the Markov approximation and weak coupling limit

Beyond the quantum Markov approximation and the weak coupling limit, we present a general theory to calculate the geometric phase for open systems with and without conserved energy. As an example, the geometric phase for a two-level system coupling both dephasingly and dissipatively to its environment is calculated. Comparison with the results from quantum trajectory analysis is presented and discussed.

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arXiv2005

A note on the geometric phase in adiabatic approximation

The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough.

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arXiv2005

Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states

Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed states. We further extend the mixed state concept proposed in [Phys. Rev. Lett. {\bf 90}, 050403 (2003)] to degenerate density operators. The first and second order off-diagonal geometric phases are analyzed for unitarily evolving pairs of pseudopure states.

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arXiv2004

Quantum nonlocality of Heisenberg XX model with Site-dependent Coupling Strength

We show that the generalized Bell inequality is violated in the extended Heisenberg model when the temperature is below a threshold value. The threshold temperature values are obtained by constructing exact solutions of the model using the temperature-dependent correlation functions. The effect due to the presence of external magnetic field is also illustrated.

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arXiv2004

Operator-sum representation of time-dependent density operators and its applications

We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples.

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arXiv2004

General formalism of Hamiltonians for realizing a prescribed evolution of a qubit

We investigate the inverse problem concerning the evolution of a qubit system, specifically we consider how one can establish the Hamiltonians that account for the evolution of a qubit along a prescribed path in the projected Hilbert space. For a given path, there are infinite Hamiltonians which can realize the same evolution. A general form of the Hamiltonians is constructed in which one may select the desired one for implementing a prescribed evolution. This scheme can be generalized to higher dimensional systems.

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arXiv2004

General Scheme for Super Dense Coding between Multi-Parties

Dense coding or super-dense coding in the case of high-dimension quantum states between two parties and multi-parties has been studied in this paper. We construct explicitly the measurement basis and the forms of the single-body unitary operations corresponding to the basis chosen, and the rules for selecting the one-body unitary operations in a multi-party case.

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