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

Toward fault-tolerant quantum computation without concatenation

It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own attractive features-improved accuracy threshold, local operations-have also been studied. By iteratively distilling a certain two-qubit entangled state it is shown how to perform an encoded Toffoli gate, important for universal computation, on CSS codes that are either unconcatenated or, for a range of very large block sizes, singly concatenated.Comment: 12 pages, 2 figures, replaced: new stuff on error models, numerical example for concatenation criteri

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 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

Controlling qubit transitions during non-adiabatic rapid passage through quantum interference

In adiabatic rapid passage, the Bloch vector of a qubit is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In non-adiabatic twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle \phi(t) at the same time that it is non-adiabatically inverted. For polynomial twist, \phi(t) \sim Bt^{n}. We show that for n \ge 3, multiple qubit resonances can occur during a single inversion of the external field, producing strong interference effects in the qubit transition probability. The character of the interference is controllable through variation of the twist strength B. Constructive and destructive interference are possible, greatly enhancing or suppressing qubit transitions. Experimental confirmation of these controllable interference effects has already occurred. Application of this interference mechanism to the construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 8 pages, 7 figures, 2 tables; submitted to J. Mod. Op

Quantum Fourier transform revisited

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank-1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix-2 QFT decomposition to a radix-d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view

Immunity of information encoded in decoherence-free subspaces to particle loss

We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU(d) unitaries, quantum superpositions stored in the decoherence free subspace are fully immune against the removal of one particle. This provides a feasible scheme to protect quantum information encoded in the polarization state of a sequence of photons against both collective depolarization and one photon loss, and can be demonstrated with photon quadruplets using currently available technology.Comment: to appear in Phys. Rev. A; 5 pages, 2 figures; content changed a bit (the property demonstrated explicitly on a 4 qubit state

Experimental quantum key distribution with active phase randomization

Phase randomization is an important assumption made in many security proofs of practical quantum key distribution (QKD) systems. Here, we present the first experimental demonstration of QKD with reliable active phase randomization. One key contribution is a polarization-insensitive phase modulator, which we added to a commercial phase-coding QKD system to randomize the global phase of each bit. We also proposed a simple but useful method to verify experimentally that the phase is indeed randomized. Our result shows very low QBER (<1%). We expect this active phase randomization process to be a standard part in future QKD set-ups due to its significance and feasibility.Comment: 3 pages, 3 figures, RevTE