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Schur-Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to…
We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties,…
Given $N_{\textrm{tot}}$ applications of a unitary operation with an unknown phase $\theta$, a large-scale fault-tolerant quantum system can {reduce} an estimate's {error} scaling from $\mathcal{O} \left[ 1 / \sqrt{N_{\textrm{tot}}}…
We prove that given the ability to make entangled measurements on at most $k$ replicas of an $n$-qubit state $\rho$ simultaneously, there is a property of $\rho$ which requires at least order $2^n$ measurements to learn. However, the same…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…
We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate…
Quantum machine learning (QML) has gained increasing attention as a potential solution to address the challenges of computation requirements in the future. Earth observation (EO) has entered the era of Big Data, and the computational…
We present a scheme for simulating the quantum network of quantum estimation proposed by A. K. Ekert et al. [Phys. Rev. Lett. 88, 217901 (2002)]. We experimentally implement the scheme with linear optical elements. We perform overlap…
Out-of-time-ordered correlators (OTOCs) are a key observable in a wide range of interconnected fields including many-body physics, quantum information science, and quantum gravity. Measuring OTOCs using near-term quantum simulators will…
Quantum tomography is one of the major challenges of large-scale quantum information research due to the exponential time complexity. In this work, we develop and apply a Bayesian state estimation method to experimentally demonstrate…
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to…
Suppose we have many copies of an unknown $n$-qubit state $\rho$. We measure some copies of $\rho$ using a known two-outcome measurement $E_{1}$, then other copies using a measurement $E_{2}$, and so on. At each stage $t$, we generate a…
Given a density operator $\hat \rho$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi \in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho $. We introduce a dual…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of…
The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation and computing. However, a full characterization of multimode quantum states requires a number of…