Related papers: Validating and Certifying Stabilizer States
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
Entangled quantum states are essential ingredients for many quantum technologies, but they must be validated before they are used. As a full characterization is prohibitively resource-intensive, recent work has focused on developing methods…
We report on experimental studies on entanglement quantification and verification based on uncertainty relations for systems consisting of two qubits. The new proposed measure is shown to be invariant under local unitary transformations, by…
We find a scaling reduction in the stabilizer rank of the twelve-qubit tensored $T$ gate magic state. This lowers its asymptotic bound to $2^{\sim 0.463 t}$ for multi-Pauli measurements on $t$ magic states, improving over the best…
Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…
We define a multi-partite entanglement measure for stabilizer states, which can be computed efficiently from a set of generators of the stabilizer group. Our measure applies to qubits, qudits and continuous variables.
Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…
Verification of quantum computations is crucial as experiments advance toward fault-tolerant quantum computing. Yet, no efficient protocol exists for certifying states generated in the Magic-State Injection model -- the foundation of…
We propose the notion of faithful coherent states based on the fidelity-based coherence witness. The criterion for detecting faithful coherent states can be restricted to a subclass of fidelity-based criterion under unitary transformations…
An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement…
Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the…
Conventionally, unknown quantum states are characterized using quantum-state tomography based on strong or weak measurements carried out on an ensemble of identically prepared systems. By contrast, the use of protective measurements offers…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the…
The stabilizer group of an n-qubit state \psi is the set of all matrices of the form g=g_1\otimes\cdots\otimes g_n, with g_1,...,g_n being any 2x2 invertible complex matrices, that satisfy g\psi=\psi. We show that for 5 or more qubits,…
The phenomenon of quantum entanglement underlies several important protocols that enable emerging quantum technologies. Entangled states, however, are extremely delicate and often get perturbed by tiny fluctuations in their external…
The Pauli stabilizer formalism is perhaps the most thoroughly studied means of procuring quantum error-correcting codes, whereby the code is obtained through commutative Pauli operators and ``stabilized'' by them. In this work we will show…
Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem…
We propose a scheme of multipartite entanglement distillation driven by a complementary pair of stabilizer measurements, to distill directly a wider range of states beyond the stabilizer code states (such as the Greenberger-Horne-Zeilinger…
We study the verification of maximally entangled states by virtue of the simplest measurement settings: local projective measurements without adaption. We show that optimal protocols are in one-to-one correspondence with complex projective…