Related papers: General detectability measure
In this thesis there are two topics: On the entangling capacity, in terms of negativity, of quantum operations, and on the supremum of negativity for symmetric Gaussian states. Positive partial transposition (PPT) states are an important…
We show a geometric formulation for minimum-error discrimination of qubit states, that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
Intrinsic randomness is generated when a quantum state is measured in any basis in which it is not diagonal. In an adversarial scenario, we quantify this randomness by the probability that a correlated eavesdropper could correctly guess the…
We study how well answer to the question ``Is the given quantum state equal to a certain maximally entangled state?'' using LOCC, in the context of hypothesis testing. Under several locality and invariance conditions, optimal tests will be…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
The are substantial studies on distinguishabilities, especially local distinguishability, of quantum states. It is shown that a necessary condition of a local distinguishable state set is the total Schmidt rank not larger than the system…
We study the problem of locally distinguishing pure quantum states using shared entanglement as a resource. For a given set of locally indistinguishable states, we define a resource state to be useful if it can enhance local…
A fundamental challenge in quantum resource theory is to establish operational interpretations by quantifying the advantage that quantum resources provide in specific tasks. Conventional resource theories, however, have inherent limitations…
Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification,…
We study the relative entropy of highly excited quantum states. First, we sample states from the Wishart ensemble and develop a large-N diagrammatic technique for the relative entropy. The solution is exactly expressed in terms of…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
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,…
State estimation for discrete-time linear systems with quantized measurements is addressed. By exploiting the set-theoretic nature of the information provided by the quantizer, the problem is cast in the set membership estimation setting.…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
We present the generalized state-dependent entropic uncertainty relations in multiple measurements setting, and the optimal lower bound is obtained by considering different measurement sequences. We then apply this uncertainty relation to…
We solve the generalised quantum Stein's lemma, proving that the Stein exponent associated with entanglement testing, namely, the quantum hypothesis testing task of distinguishing between $n$ copies of an entangled state $\rho_{AB}$ and a…