The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe overhead in terms of the accumulation of errors. Here we describe an method that can rapidly generate large entangled states with an error accumulation that depends only logarithmically on the failure probability. We find that the approach may be practical for success rates in the sub-10% range, while ultimately becoming unfeasible at lower rates. The assumptions that we make, including parallelism and high connectivity, are appropriate for real systems including measurement-induced entanglement. This result therefore shows the feasibility for real devices based on such an approach.
Recently, the nonlocal optimal probabilistic cloning (NLOPC) of two non-orthogonal qubit states has been proposed [Phys. Rev. A 86, 052332 (2012)] by means of an experimental setup based on a pair of twin photons in a maximally entangled state. Here we study the performance of the NLOPC protocol when implemented via a partially entangled state. We show that the errors introduced by the use of partial entanglement can be undone by applying a quantum state discrimination process. Since quantum state discrimination is a probabilistic process the correction succeeds with a certain probability but …
A scheme is proposed to entangle two systems that have not interacted by using an ancillary particle in a Mach-Zehnder interferometer, by making a suitable post--selection of the particle followed by a conditional feedback on one of the subsystems to be entangled. For a strong interaction, the process works deterministically. For a weaker interaction only the probability of success is reduced, but the output continues to be a maximally entangled state.
We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $σ_{x}$. Both these measurement outcomes are communicated to Bob classical…
Teleporation with partially entangled quantum channel cannot achieve unit fidelity and unit probability. We show that the conditions for faithful teleportation of a pure state or a mixed state can be described by the same general relation $ρ_{q}ρ_{m} = pI$, where $ρ_{q}$ is the reduced density matrix of the quantum channel, $ρ_{m}$ is the reduced density matrix of the measurement basis, and $p$ is the probability of faithful teleportaion. We investigate the invariance of faithful teleportation conditions under unitary transformation. These results not only bring new insights to the probabilist…
Double Covariance Model for Entangled Quantum States: Gaussian Reduction to Second Order Covariances
Center for Mathematical Modeling in Physics and Cognitive Sciences（物理与认知科学数学建模中心）；Institute for Mathematics and Physics, Linnaeus University（林奈大学数学与物理研究所）
Using only linear optical elements, the creation of dual-rail photonic entangled states is inherently probabilistic. Known entanglement generation schemes have low success probabilities, requiring large-scale multiplexing to achieve near-deterministic operation of quantum information processing protocols. In this paper, we introduce multiple techniques and methods to generate photonic entangled states with high probability, which have the potential to reduce the footprint of Linear Optical Quantum Computing (LOQC) architectures drastically. Most notably, we are showing how to improve Bell stat…
We study the probabilistic (conditional) teleportation protocol when the entanglement needed to its implementation is given by thermal entanglement, i.e., when the entangled resource connecting Alice and Bob is an entangled mixed state described by the canonical ensemble density matrix. Specifically, the entangled resource we employ here is given by two interacting spin-1/2 systems (two qubits) in equilibrium with a thermal reservoir at temperature T. The interaction between the qubits is described by a Heisenberg-like Hamiltonian, encompassing the Ising, the XX, the XY, the XXX, and XXZ model…
