Related papers: Upper and Lower Bounds on Optimal Success Probabil…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are…
We study the problem of discriminating between non-orthogonal quantum states with least probability of error. We demonstrate that this problem can be simplified if we solve for the error itself rather than solving directly for the optimal…
We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence…
Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit…
In this paper by using geometric techniques, we provide upper bounds for the Poincar\'e recurrence time of a quantum mixed state with discrete spectrum of energies. In the case of discrete but finite spectrum we obtain two type of upper…
We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for…
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…
The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest…
We relate the the distinguishability of quantum states with their robustness of the entanglement, where the robustness of any resource quantifies how tolerant it is to noise. In particular, we identify upper and lower bounds on the…
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 study the fully entangled fraction of quantum states. An upper bound is obtained for arbitrary dimensional bipartite systems. This bound is shown to be exact for the case of two-qubit systems. An inequality related the fully entangled…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We propose two experimental schemes for quantum state discrimination that achieve the optimal tradeoff between the probability of correct identification and the disturbance on the quantum state.
We investigate the ability of a quantum measurement device to discriminate two states or, generically, two hypothesis. In full generality, the measurement can be performed a number $n$ of times, and arbitrary pre-processing of the states…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
We obtain an analytical lower bound of entanglement quantified by concurrence for arbitrary bipartite quantum states. It is shown that our bound is tight for some mixed states and is complementary to the previous known lower bounds. On the…