Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building universal computer. In this review we consider the formalism of and subsystem their possible use in protecting information memory. We theory fault-tolerance error-correction, discuss examples various code constructions, general conditions, noise threshold, special role played by Clifford gates route towards fault-tolerant computation. The...

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but sender knows classically what is be transmitted. We show that asymptotic cost RSP bit per qubit--half teleportation--and even less when transmitting part a known entangled explore tradeoff between required for RSP, discuss capacities general channels.

An unextendible product basis (UPB) for a multipartite quantum system is an incomplete orthogonal whose complementary subspace contains no state. We give examples of UPBs, and show that the uniform mixed state over to any UPB bound entangled exhibit tripartite 2x2x2 has entanglement but bipartite entanglement, i.e. all three corresponding 2x4 states are unentangled. members not perfectly distinguishable by local POVMs classical communication.

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- binomial-code proposals. Numerically optimized codes have also proposed, we introduce of this type here. These yet to be compared using the same error model; provide such comparison determining entanglement fidelity all with respect bosonic pure-loss channel (i.e., photon loss) after optimal recovery operation. We then compare achievable communication rates...

Abstract Solid-state spin qubits is a promising platform for quantum computation and networks 1,2 . Recent experiments have demonstrated high-quality control over multi-qubit systems 3–8 , elementary algorithms 8–11 non-fault-tolerant error correction 12–14 Large-scale will require using error-corrected logical that are operated fault tolerantly, so reliable becomes possible despite noisy operations 15–18 Overcoming imperfections in this way remains an important outstanding challenge science...

Conditional-phase (cz) gates in transmons can be realized by flux pulsing computational states towards resonance with noncomputational ones. We present a 40 ns cz gate based on bipolar pulse suppressing leakage (0.1%) interference and approaching the speed limit set exchange coupling. This harnesses built-in echo to enhance fidelity (99.1%) is robust long-timescale distortion flux-control line, ensuring repeatability. Numerical simulations matching experiment show that limited high-frequency...

We introduce the notion of a Schmidt number bipartite density matrix. show that k-positive maps witness number, in same way positive entanglement. determine family states is made from mixing completely mixed state and maximally entangled state. does not necessarily increase when taking tensor copies matrix $\ensuremath{\rho};$ we give an example for which numbers $\ensuremath{\rho}$ $\ensuremath{\rho}\ensuremath{\bigotimes}\ensuremath{\rho}$ are both $2.$

We give a detailed proof of the conjecture that asymptotic entanglement cost preparing bipartite state ρis equal to regularized formation ρ.

We show that a class of quantum computations was recently shown to be efficiently simulatable on classical computer by Valiant corresponds physical model noninteracting fermions in one dimension. give an alternative proof his result using the language and extend with arbitrary pairwise interactions, where gates can conditioned outcomes complete von Neumann measurements computational basis other fermionic modes circuit. This last is remarkable contrast case bosons universal computation...

We expand on our work Quantum Data Hiding -- hiding classical data among parties who are restricted to performing only local quantum operations and communication (LOCC). review scheme that hides one bit between two using Bell states, we derive upper lower bounds the secrecy of scheme. provide an explicit bound showing multiple bits can be hidden bitwise with give a preparation states as efficient computation uses at most ebit entanglement. A candidate does not use entanglement is presented....

We introduce a measure of both quantum as well classical correlations in state, the entanglement purification. show that (regularized) purification is equal to cost creating state ρ asymptotically from maximally entangled states, with negligible communication. prove mutual information and divided by two are lower bounds for regularized present numerical results Werner states H2⊗H2.

We present a scheme for hiding bits in Bell states that is secure even when the sharers, Alice and Bob, are allowed to carry out local quantum operations classical communication. prove information Bob can gain about hidden bit exponentially small $n$, number of qubits each share, be made arbitrarily multiple bits. indicate an alternative efficient low-entanglement method preparing shared states. discuss how our implemented using present-day optics.

We give an explicit expression for the entanglement of formation isotropic density matrices in arbitrary dimensions terms convex hull a simple function. For two qutrit states we determine and have strong evidence its exact form dimension. Unlike qubits, qutrits or more is found to be nonanalytic function maximally entangled fraction regime where matrix entangled.

We show that there exist bipartite quantum states which contain a large locked classical correlation is unlocked by disproportionately small amount of communication. In particular, are (2n+1)-qubit for one-bit message doubles the optimal mutual information between measurement results on subsystems, from n/2 bits to n bits. This phenomenon impossible classically. However, exhibiting this behavior need not be entangled. study range and bound its magnitude.

We exhibit a two-parameter family of bipartite mixed states $\rho_{bc}$, in $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for we conjecture that no maximally entangled pure $2\otimes 2$ can be distilled by local quantum operations and classical communication (LQ+CC). Evidence this undistillability is provided the result that, certain family, cannot extract entanglement from any arbitrarily large number copies $\rho_{bc}$ using projection on 2$. These...

In this paper I discuss some of the early history quantum information theory. By considering question whether entanglement is “monogamous,” illustrate Charles Bennett's influence on modern Finally, review our recent answers to and its relation Bell inequalities.

We derive a threshold result for fault-tolerant quantum computation local non-Markovian noise models. The role of error amplitude in our analysis is played by the product elementary gate time ${t}_{0}$ and spectral width interaction Hamiltonian between system bath. discuss extensions model applicability analysis.

We study the complexity of Local Hamiltonian Problem (denoted as LH-MIN) in special case when a obeys condition that all off-diagonal matrix elements standard basis are real and non-positive. will call such Hamiltonians, which common natural world, stoquastic. An equivalent characterization stoquastic Hamiltonians is they have an entry-wise non-negative Gibbs density for any temperature. prove LH-MIN belongs to class AM -- probabilistic version NP with two rounds communication between prover...

The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantumcomputational class QMA [1]. In this paper we show that important problemremains QMA-complete when interactions of 2-local Hamiltonian are betweenqubits on a two-dimensional (2-D) square lattice. Our results partially derived withnovel perturbation gadgets employ mediator qubits which allow us manipulatek-local interactions. As side result, obtain quantum adiabatic computationusing restricted 2-D lattice is...