The estimation of multiple parameters in quantum metrology is important for a vast array applications information processing. However, the unattainability fundamental precision bounds incompatible observables has greatly diminished applicability theory many practical implementations. Holevo Cramer-Rao bound (HCRB) provides most fundamental, simultaneously attainable multi-parameter problems. A general closed form HCRB not known given that it requires complex optimisation over variables. In...

A quantum code is a subspace of Hilbert space physical system chosen to be correctable against given class errors, where information can encoded. Ideally, the lies within ground system. When model Heisenberg ferromagnet in absence an external magnetic field, corresponding contains all permutation-invariant states. We use techniques from combinatorics and operator theory construct families codes. These codes have length proportional ${t}^{2}$; one family perfectly corrects arbitrary weight...

The recent discovery of fully homomorphic classical encryption schemes has had a dramatic effect on the direction modern cryptography. Such schemes, however, implicitly rely assumption that solving certain computation problems is intractable. Here we present quantum scheme which for arbitrary and circuits have at most some constant number non-Clifford gates. Unlike security information theoretic hence independent computational power an adversary.

Encryption schemes often derive their power from the properties of underlying algebra on symbols used. Inspired by group theoretic tools, we use centralizer a subgroup operations to present private-key quantum homomorphic encryption scheme that enables broad class computation encrypted data. The data is encoded bosons distinct species in spatial modes, and computations are manipulations these manner independent species. A particular instance our encoding hides up constant fraction...

Simulation of quantum chemistry is expected to be a principal application computing. In simulation, complicated Hamiltonian describing the dynamics system decomposed into its constituent terms, where effect each term during time-evolution individually computed. For many physical systems, has large number constraining scalability established simulation methods. To address this limitation we introduce new scheme that approximates actual with sparser containing fewer terms. By stochastically...

Security proofs that incorporate physical constraints of realistic heterodyne detectors are presented, establishing a rigorous analysis collective attacks in continuous-variable quantum cryptography scheme.

In the quest to unlock maximum potential of quantum sensors, it is paramount importance have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, still not known how find measurements optimal precisions, even for uncorrelated over probe states. Here, we give a concrete way precisions. We solve this fundamental problem by introducing framework conic programming unifies theory precision bounds multiparameter estimates and correlated...

We must protect inherently fragile quantum data to unlock the potential of technologies. A pertinent concern in schemes for storage is their near-term implementation. Since Heisenberg ferromagnets are readily available, we investigate robust storage. propose use permutation-invariant codes store ferromagnets, because ground space any ferromagnet be symmetric under permutation underlying qubits. By exploiting an area law on expected energy Pauli errors, show that increasing effective...

Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of error correction procedures, near term devices are expected to noisy, and we have make do noisy probe states. We prove that, set carefully chosen symmetric states that lie within certain codes, exhibits an advantage over classical even after the corrupted by constant number erasure dephasing errors. These useful robust not only in...

We introduce and analyze approximate quantum secret sharing in a formal cryptographic setting, wherein dealer encodes distributes to players such that authorized structures (sets of subsets players) can approximately reconstruct the omnipotent adversarial agents controlling nonauthorized are denied secret. In particular, viewing map encoding shares for an structure as channel, we show reconstructability by these is possible if only information leakage, given terms certain...

Following the emergence of quantum computing, subsequent revolution will be that interconnecting individual computers at global level. In same way classical only realised their full potential with internet, a fully internet is next stage evolution for computation. This work examines in detail how would evolve practice, focusing not on technology itself but also implications it have economically and politically. We present both original ideas, as well an extensive review relevant related...

A permutation-invariant code on $m$ qubits is a subspace of the symmetric qubits. We derive codes that can encode an increasing amount quantum information while suppressing leading-order spontaneous decay errors. To prove result, we use elementary number theory with prior and error correction.

The capacity of a channel is known to be equivalent the highest rate at which it can generate entanglement. Analogous entanglement, notion causality measure characterizes temporal aspect quantum correlations. Despite holding an equally fundamental role in physics, correlations have yet find their operational significance communication. Here we uncover connection between and capacity. We show amount two ends noisy channel, as quantified by measure, implies general upper bound on its...

Consumption of magic states promotes the stabilizer model computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such circuits, and characterize them by establishing precise connections with a family monotones. Our first simulator introduces new class quasiprobability distributions connects its runtime generalized notion negativity. We prove that this algorithm has significantly improved exponential scaling compared all prior...

Evaluating the quantum capacity of channels is an important but difficult problem, even for low input and output dimension. Smith Smolin showed that Clifford-twirl a qubit amplitude damping channel (a depolarizing channel) has at most coherent information evaluated on maximally mixed state. We restrict our attention to obtaining upper bounds using generalization Smolin's degradable extension technique. Given $\cN$ finite projective group unitaries $\cV$, we show $\cV$-twirl maximized over...

Quantum deletions, which are harder to correct than erasure errors, occur in many realistic settings. It is therefore pertinent develop quantum coding schemes for deletion channels. To date, not much known about explicit error correction codes can combat deletions. We note that any permutation-invariant code has a distance of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t+1$</tex> xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex>...

The development of high-resolution, large-baseline optical interferometers would revolutionize astronomical imaging. However, classical techniques are hindered by physical limitations including loss, noise, and the fact that received light is generally quantum in nature. We show how to overcome these issues using communication techniques. present a general framework for error correction codes protecting imaging starlight at distant telescope sites. In our scheme, state coherently captured...

The increasing interest in using quantum error correcting codes practical devices has heightened the need for designing that can correct against specialized errors, such as of amplitude damping errors which model photon loss. Although considerable research been devoted to damping, not so much attention paid having these simultaneously lie within decoherence free subspace their underlying physical system. One common system comprises harmonic oscillators, and constant-excitation be naturally...

We give a polynomial-time algorithm for computing upper bounds on some of the smaller energy eigenvalues in spin-1/2 ferromagnetic Heisenberg model with any graph $G$ underlying interactions. An important ingredient is connection between models and symmetric products $G$. Our algorithms are based generalized diameters graphs. Computing amounts to solving minimum assignment problem $G$, which has well-known from field combinatorial optimization. also study possibility lower models. This...

Abstract Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation by code concatenation. Namely, concatenating an [[ n , k d ]] outer dual-rail inner codes, obtain [[2 immune coherent phase errors also equivalent to Pauli-rotated code. When the is fault-tolerant, has positive fault-tolerant threshold...

Recently, there has been growing interest in using quantum error correction practical devices. A central issue is the initialization of data into a error-correction code. Most studies have concentrated on generating codes based their encoding circuits. However, this often leads to large number steps required initialization, and hence process can be prone errors. The purpose work demonstrate that permutation-invariant created with high fidelity by exploiting underlying symmetry. code...

A family of quantum codes increasing block length with positive rate is asymptotically good if the ratio its distance to approaches a constant. The asymptotic Gilbert-Varshamov (GV) bound states that there exist q -ary sufficiently long N having fixed R at least NH <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ((1-R)/2), where H <sub xmlns:xlink="http://www.w3.org/1999/xlink">q2</sub> xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>...

We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The operations require only rotations in phase space, which commute with computations the code space performed via passive linear optics, and generalized nonlinear that are polynomials of photon-number operator space. This encoding can thus be applied to any computation coherent-state inputs, proceeds combination optics operations. An example such is matrix multiplication, whereby...

A (k,n)-threshold secret-sharing scheme allows for a string to be split into n shares in such way that any subset of at least k suffices recover the secret string, but most k-1 contains no information about secret. Quantum schemes extend this idea sharing quantum states. Here we propose method performing computation on shared secrets. We introduce (n,n)-quantum together with set protocols allow circuits evaluated without need decode consider multipartite setting, each participant holding...