Related papers: Comparing the states of many quantum systems
We introduce and analyze a task that we call symmetrization, in which a state of a quantum system, associated with a symmetry group, is transformed by a random unitary operation to a symmetric state. Each element of the unitary ensemble is…
In this paper, we consider the problem of unambiguous discrimination between a set of mixed quantum states. We first divide the density matrix of each mixed state into two parts by the fact that it comes from ensemble of pure quantum…
Accurately estimating the overlap between quantum states is a fundamental task in quantum information processing. While various strategies using distinct quantum measurements have been proposed for overlap estimation, the lack of…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain…
We consider the problem of unambiguous (error-free) discrimination of N linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
Unambiguous discrimination and exact cloning reduce the square-overlap between quantum states, exemplifying the more general type of procedure we term state separation. We obtain the maximum probability with which two equiprobable quantum…
The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While…
In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has…
Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups,…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
Is there any point of principle that prohibits us from doing one or more forms of quantum information processing? It is now well known that an unknown quantum state can neither be copied nor deleted perfectly. Given a set of states which…
Quantum information theory sets the ultimate limits for any information-processing task. In rangefinding and LIDAR, the presence or absence of a target can be tested by detecting different states at the receiver. In this Letter, we use…
The goal of quantum benchmarking is to certify that imperfect quantum communication devices (e.g., quantum channels, quantum memories, quantum key distribution systems) can still be used for meaningful quantum communication. However, the…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…