Mathematical and Computational Sciences Division,

National Institute of Standards and Technology,

Gaithersburg, MD 20899-8910

Phone: (301) 975-4618

Fax: (301) 990-4127

Email:dsong@nist.gov

- Centre for Quantum Computation, University of Oxford, Ph.D (2001).

- NRC Research (Postdoctoral) Associate

Research and Publications

- D. Song
**Secure Key Distribution by Swapping Quantum Entanglement**

submitted to Phys. Rev. Lett.

Preprint: quant-ph/0305168*Abstract*: We report two key distribution schemes achieved by swapping quantum entanglement. Using two Bell states, two bits of secret key can be shared between two distant parties that play symmetric and equal roles. We address eavesdropping attacks against the schemes and show that improved chances of detecting them can be achieved with fewer resources than previously proposed protocols.

- D. Song
**Post-measurement Nonlocal Gates**

submitted to J. Opt. B

Preprint: quant-ph/0303147*Abstract*: Several proposed quantum computer models include measurement processes, in order to implement nonlocal gates and create necessary entanglement resources during the computation. We introduce a scheme in which the measurements can be delayed for two- and three-qubit nonlocal gates. We also discuss implementing arbitrary nonlocal gates when measurements are included during the process. - D. Song
**Remarks on Entanglement Swapping**

to appear in J. Opt. B*Abstract*: In two partially entangled states, entanglement swapping by Bell measurement will yield weaker entanglement between the two. We know this scheme is optimal because the average entanglement cannot increase under local operation and classical communication. However, for more than two states, this scheme does not always yield the weakest link. We consider other projective measurements besides Bell-type measurement and show , numerically, that Bell measurement is indeed optimal among these projective measurements. - G.K. Brennen, D. Song and C.J. Williams
**Quantum Computer Architecture using Nonlocal Operations**

Phys. Rev. A 67, 050302(R) (2003).

Preprint: quant-ph/0301012

Newsfactor: Quantum Bits need to catch a Virtual Bus

TRNmag.com: Quantum computing catches the bus

*Abstract*Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper we propose a physical solution to this problem which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers. - G.K. Brennen, D. Song and C.J. Williams
**A Scalable Quantum Architecture using Efficient Nonlocal Interactions**

Proceedings of Quantum Communication, Measurement & Computation, edited by J.H. Shapiro and O. Hirota, p201, (2002).*Abstract*: Manhy protocols for quantum information processing use a control sequence or circuit of interactions between qubits and control fields wherein arbitrary qubits can be made to interact with one another. The primary problem with many "physically scalable" architectures is that the qubits are restricted to nearest neighbor interactions and quantum wires between distant qubits do not exit. Because of errors, nearest neighbor interactions often present difficulty with scalability. In this paper we describe a generalized quantum architecture that provides efficient nonlocal operations for such a system. We describe a protocol that efficiently performs nonlocal gates between elements of separated static logical qubits using a bus of dynamic qubits that can be used as a refreshable entanglement resource. - G.K. Brennen and D. Song
**Entanglement Resources in Quantum Computing**

Preprint:*Abstract*: Many protocols for quantum information processing (QIP) use a control sequence or circuit of interactions between qubits and control fields wherein arbitrary qubits can be made to interact with one another. Often the errors that accumulate in these schemes fall into two distinct classes: static errors which occur when the qubits are fixed and non-interacting with other qubits, and dynamic errors accumulated during single and two qubit operations or during the transmission of quantum information either by physically moving the qubits or swapping information from one location to another. The chosen architecture in which to perform QIP given a physical system will depend on which errors will dominate in that system for a given task. We investigate protocols to efficiently perform nonlocal gates between separated static logical qubits using a bus of dynamic qubits that can be used as a refreshable entanglement resource. In particular, entanglement swapping methods are used to create the necessary network among dynamic qubits. A scheme to perform a nondeterministic nonlocal Toffoli gate using a multibody entangled resource is given. This protocol is shown to be valuable as a technique to simulate nonlocal decoherence. The noise is produced by a nonfactorisable superoperator acting as phase noise over the qubits. It is shown that this noise can be coherently triggered by one or more qubits. - D. Song and R.J. Szabo
**Duality and Decoherence Free Subspaces**

Preprint: quant-ph/0011021*Abstract*: Quantum error avoiding codes are constructed by exploiting a geometric interpretation of the algebra of measurements of an open quantum system. The notion of a generalized Dirac operator is introduced and used to naturally construct families of decoherence free subspaces for the encoding of quantum information. The members of the family are connected to each other by the discrete Morita equivalences of the algebra of observables, which render possible several choices of noiseless code in which to perform quantum computation. The construction is applied to various examples of discrete and continuous quantum systems.

- L. Hardy and D. Song
**Nonlinear Qubit Transformations**

Phys. Rev. A 64, 032301 (2001)

Preprint: quant-ph/0102100*Abstract*: We generalise our previous results of universal linear manipulations [Phys. Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are studied. We rotate different parts of a Bloch sphere in opposite directions about the z-axis. The second transformation is a map which sends a qubit to its orthogonal state (which we define as ORTHOG). We consider the case when the ORTHOG is applied to only a partial area of a Bloch sphere. We also study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi), again, applied only to part of the Bloch sphere. In order to achieve these three operations, we consider different measurement preparations and derive the optimal average (instead of universal) quantum unitary transformations. We also introduce a simple method for a qubit measurement and its application to other cases. - L. Hardy and D. Song
**Universal Manipulation of a Single Qubit**

Phys. Rev. A 63, 032304 (2001)

Preprint: quant-ph/0008011*Abstract*We find the optimal universal way of manipulating a single qubit, |psi(theta,phi)>, such that (theta,phi)->(theta-k,phi-l). Such optimal transformations fall into two classes. For 0 =< k =< pi/2 the optimal map is the identity and the fidelity varies monotonically from 1 (for k=0) to 1/2 (for k=pi/2). For pi/2 =< k =< pi the optimal map is the universal-NOT gate and the fidelity varies monotonically from 1/2 (for k=pi/2) to 2/3 (for k=pi). The fidelity 2/3 is equal to the fidelity of measurement. It is therefore rather surprising that for some values of k the fidelity is lower than 2/3. - L. Hardy and D. Song
**Entanglement Swapping Chains for General Pure States**

Phys. Rev. A 62, 052315 (2000)

Preprint: quant-ph/0006132*Abstract*We consider entanglement swapping schemes with general (rather than maximally) entangled bipartite states of arbitary dimension shared pairwise between three or more parties in a chain. The intermediate parties perform generalised Bell measurements with the result that the two end parties end up sharing a entangled state which can be converted into maximally entangled states. We obtain an expression for the average amount of maximal entanglement concentrated in such a scheme and show that in a certain reasonably broad class of cases this scheme is provably optimal and that, in these cases, the amount of entanglement concentrated between the two ends is equal to that which could be concentrated from the weakest link in the chain. - L. Hardy and D. Song
**Quantum Anti-Cloning**

Preprint: quant-ph/0001105*Abstract*We derive the transformation for the optimal universal quantum anti-cloner which produces two anti-parallel outputs for a single input state. The fidelity is shown to be 2/3 which is same as the measurement fidelity. We consider a probabilistic quantum anti-cloner and show quantum states can be anti-cloned exactly with non-zero probability and its efficiency is higher than the efficiency of distinguishing between the two states. - L. Hardy and D. Song
**No Signalling and Probabilistic Quantum Cloning**

Phys.Lett. A259 (1999) 331-333

Preprint: quant-ph/9905024*Abstract*We show that the condition of no faster-than-light signalling restricts the number of quantum states that can be cloned in a given Hilbert space. This condition leads to the constraints on a probabilistic quantum cloning machine (PQCM) recently found by Duan and Guo.

- D. Song and E. Winstanley:
**Information Erasure and the Generalized Second Law of Black Hole Thermodynamics**

Preprint: gr-qc/0009083*Abstract:*We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer's principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer's principle. - D. Song and R.J. Szabo:
**Spectral Geometry of Heterotic Compactifications**

Class.Quant.Grav. 16 (1999) 3013-3024*Abstract:*The structure of heterotic string target space compactifications is studied using the formalism of the noncommutative geometry associated with lattice vertex operator algebras. The spectral triples of the noncommutative spacetimes are constructed and used to show that the intrinsic gauge field degrees of freedom disappear in the low-energy sectors of these spacetimes. The quantum geometry is thereby determined in much the same way as for ordinary superstring target spaces. In this setting, non-abelian gauge theories on the classical spacetimes arise from the K-theory of the effective target spaces. - D. Song and R.J. Szabo:
**Black String Entropy from Anomalous D-brane Couplings**

Eur.Phys.J. C13 (2000) 641-646*Abstract:*The quantum corrections to the counting of statistical entropy for the 5+1-dimensional extremal black string in type-IIB supergravity with two observers are studied using anomalous Wess-Zumino actions for the corresponding intersecting D-brane description. The electric-magnetic duality symmetry of the anomalous theory implies a new symmetry between D-string and D-fivebrane sources and renders opposite sign for the RR charge of one of the intersecting D-branes relative to that of the black string. The electric-magnetic symmetric Hilbert space decomposes into subspaces associated with interior and exterior regions and it is shown that, for an outside observer, the expectation value of a horizon area operator agrees with the deviation of the classical horizon area in going from extremal to near-extremal black strings.

Last updated on September, 2003.