Related papers: Distinguishing mixed quantum states: Minimum-error…
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…
In this paper, we discuss the problem of determining whether a quantum system is in a pure state, or in a mixed state. We apply two strategies to settle this problem: the unambiguous discrimination and the maximum confidence discrimination.…
We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space…
In this work we relate the well-known no-go theorem that two non-orthogonal (mixed) quantum states cannot be perfectly discriminated, to the general principle in physics, the no-signalling condition. In fact, we derive the minimum error in…
We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary $m$ mixed quantum states with given prior probabilities. When $m=2$, this bound is precisely the well-known Helstrom…
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 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…
We provide a solution of finding optimal measurement strategy for distinguishing between symmetric mixed quantum states. It is assumed that the matrix elements of at least one of the symmetric quantum states are all real and nonnegative in…
We have investigated the problem of discriminating between nonorthogonal quantum states with least probability of error. We have determined that the best strategy for some sets of states is to make no measurement at all, and simply to…
The optimal discrimination of non-orthogonal quantum states with minimum error probability is a fundamental task in quantum measurement theory as well as an important primitive in optical communication. In this work, we propose and…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
Recently the problem of Unambiguous State Discrimination (USD) of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [1]. For two mixed states they are given in terms of…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
We consider a state discrimination problem which deals with settings of minimum-error and unambiguous discrimination systematically by introducing a margin for the probability of an incorrect guess. We analyze discrimination of three…
We provide a bound on the minimum error when discriminating among quantum states, using the no-signaling principle. The bound is general in that it depends on neither dimensions nor specific structures of given quantum states to be…
We present the conditions under which probabilistic error-free discrimination of mixed states is possible, and provide upper and lower bounds on the maximum probability of success for the case of two mixed states. We solve certain special…
We study an optimized measurement which discriminates N mixed quantum states occurring with given prior robabilities. The measurement yields the maximum achievable confidence for each of the N conclusive outcomes, thereby keeping the…
We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the…
In this article, we study the problem of comparing mixed quantum states: given $n$ unknown mixed quantum states, can one determine whether they are identical or not with an unambiguous quantum measurement? We first study universal…
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,…