arXiv subjects

David D. Song

Publications and source records attributed to David D. Song.

9 recordsLinked to original sources

arXiv2001

Nonlinear Qubit Transformations

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.

quant-ph↗

arXiv2000

Duality and Decoherence Free Subspaces

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.

quant-ph↗

arXiv2000

Information Erasure and the Generalized Second Law of Black Hole Thermodynamics

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.

gr-qc↗

arXiv2000

Universal Manipulation of a Single Qubit

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.

quant-ph↗

arXiv2000

Entanglement Swapping Chains for General Pure States

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.

quant-ph↗

arXiv2000

Quantum Anti-Cloning

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.

quant-ph↗

arXiv1999

No Signalling and Probabilistic Quantum Cloning

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.

quant-ph↗

arXiv1998

Spectral Geometry of Heterotic Compactifications

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.

hep-th↗

arXiv1998

Black String Entropy from Anomalous D-brane Couplings

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.

hep-th↗