Related papers: Helstrom's Theory on Quantum Binary Decision Revis…
Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…
We present a general formalism for charecterizing 2-time quantum states, describing pre- and post-selected quantum systems. The most general 2-time state is characterized by a `density vector' that is independent of measurements performed…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Quantum parameter estimation holds significant promise for achieving high precision through the utilization of the most informative measurements. While various lower bounds have been developed to assess the best accuracy for estimates, they…
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. It is far less common to exploit non-Hermitian operators to perform measurements. Here, we show…
Quantum tomography has become an indispensable tool in order to compute the density matrix $\rho$ of quantum systems in Physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
A quantum algorithm for computing the determinant of a unitary matrix $U\in U(N)$ is given. The algorithm requires no preparation of eigenstates of $U$ and estimates the phase of the determinant to $t$ binary digits accuracy with…
Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete…
Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct with high fidelity,…
The problem addressed is to design a detector which is maximally sensitive to specific quantum states. Here we concentrate on quantum state detection using the worst-case a posteriori probability of detection as the design criterion. This…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations,…
The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
We introduce and experimentally demonstrate a technique for performing quantum state tomography on multiple-qubit states despite incomplete knowledge about the unitary operations used to change the measurement basis. Given unitary…
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multi-copy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom…
In this work, we introduce an original self-consistent scheme based on the one-body reduced density matrix ($\gamma$) formalism. A significant feature of this methodology is the utilization of an optimal unitary transformation of the…
Strategies to optimally discriminate between quantum states are critical in quantum technologies. We present an experimental demonstration of minimum error discrimination between entangled states, encoded in the polarization of pairs of…
The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed…