On the Mass of M31

Recent work by several groups has established the properties of the dwarf satellites to M31. We reexamine the reported kinematics of this group employing a fresh technique we have developed previously. By calculating the distribution of a chi statistic (which we define in the paper) for the M31 system, we conclude that the total mass (disk plus halo) of the primary is unlikely to be as great as that of our own Milky Way. In fact the chi distribution for M31 indicates that, like NGC 3992, it does not have a massive halo. In contrast, the analysis of the satellites of NGC 1961 and NGC 5084 provides strong evidence for massive halos surrounding both spiral galaxies.Comment: To appear in MNRAS, 10 pages with 6 figure

Improvement of stabilizer based entanglement distillation protocols by encoding operators

This paper presents a method for enumerating all encoding operators in the Clifford group for a given stabilizer. Furthermore, we classify encoding operators into the equivalence classes such that EDPs (Entanglement Distillation Protocol) constructed from encoding operators in the same equivalence class have the same performance. By this classification, for a given parameter, the number of candidates for good EDPs is significantly reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]] stabilizer codes. This EDP has a better performance than previously known EDPs over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding operators in the Clifford group, and fix the wrong classification of encoding operators in version

Robust polarization-based quantum key distribution over collective-noise channel

We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems, and so can function over a quantum channel subjected to an arbitrary degree of collective noise, as occurs, for instance, due to rotation of polarizations in an optical fiber. These protocols can be implemented using only entangled photon-pair sources, single-photon rotations, and single-photon detectors. Thus, our proposals offer practical and realistic alternatives to existing schemes for quantum key distribution over optical fibers without resorting to interferometry or two-way quantum communication, thereby circumventing, respectively, the need for high precision timing and the threat of Trojan horse attacks.Comment: Minor changes, added reference

Quantum Teleportation is a Universal Computational Primitive

We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.Comment: 6 pages, REVTeX, 6 epsf figure

Robust randomized benchmarking of quantum processes

We describe a simple randomized benchmarking protocol for quantum information processors and obtain a sequence of models for the observable fidelity decay as a function of a perturbative expansion of the errors. We are able to prove that the protocol provides an efficient and reliable estimate of an average error-rate for a set operations (gates) under a general noise model that allows for both time and gate-dependent errors. We determine the conditions under which this estimate remains valid and illustrate the protocol through numerical examples.Comment: 4+ pages, 1 figure, and 1 tabl

Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code

Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single qubit errors and measure the fidelity of the encoded logical gate operations

Spectral Effects of Strong Chi-2 Non-Linearity for Quantum Processing

Optical $\chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency response. It is therefore of interest to know how spectral effects of a strong $\chi^{(2)}$ crystal affect the performance. Here we model the spectral effects of the dispersion of a strong $\chi^{(2)}$ crystal and illustrate how this affects its ability to perform Bell measurements and influence the performance of a quantum gates that employ such a Bell measurement. We show that a Dyson series expansion of the unitary operator is necessary in general, leading to unwanted spectral entanglement. We identify a limiting situation employing periodic poling, in which a Taylor series expansion is a good approximation and this entanglement can be removed.Comment: Will be submitted to PR

GHZ extraction yield for multipartite stabilizer states

Let $|\Psi>$ be an arbitrary stabilizer state distributed between three remote parties, such that each party holds several qubits. Let $S$ be a stabilizer group of $|\Psi>$. We show that $|\Psi>$ can be converted by local unitaries into a collection of singlets, GHZ states, and local one-qubit states. The numbers of singlets and GHZs are determined by dimensions of certain subgroups of $S$. For an arbitrary number of parties $m$ we find a formula for the maximal number of $m$-partite GHZ states that can be extracted from $|\Psi>$ by local unitaries. A connection with earlier introduced measures of multipartite correlations is made. An example of an undecomposable four-party stabilizer state with more than one qubit per party is given. These results are derived from a general theoretical framework that allows one to study interconversion of multipartite stabilizer states by local Clifford group operators. As a simple application, we study three-party entanglement in two-dimensional lattice models that can be exactly solved by the stabilizer formalism.Comment: 12 pages, 1 figur

Greenberger-Horne-Zeilinger paradoxes for many qudits

We construct GHZ contradictions for three or more parties sharing an entangled state, the dimension d of each subsystem being an even integer greater than 2. The simplest example that goes beyond the standard GHZ paradox (three qubits) involves five ququats (d=4). We then examine the criteria a GHZ paradox must satisfy in order to be genuinely M-partite and d-dimensional.Comment: 5 pages RevTe