Related papers: Comparing the states of many quantum systems
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
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…
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 study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
We present a solution of the problem of the optimal unambiguous comparison of two ensembles of unknown quantum states (psi_1)^k and (psi_2)^l. We consider two cases: 1) The two unknown states psi_1 and psi_2 are arbitrary states of qudits.…
The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether $n$ unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or…
We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result.…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
Suppose that three kinds of quantum systems are given in some unknown states $\ket f^{\otimes N}$, $\ket{g_1}^{\otimes K}$, and $\ket{g_2}^{\otimes K}$, and we want to decide which \textit{template} state $\ket{g_1}$ or $\ket{g_2}$, each…
Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…
The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can…
Quantum machine learning seeks a computational advantage in data processing by evaluating functions of quantum states, such as their similarity, that can be classically intractable to compute. For quantum advantage to be possible, however,…
We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
It is a fundamental consequence of the superposition principle for quantum states that there must exist non-orthogonal states, that is states that, although different, have a non-zero overlap. This finite overlap means that there is no way…
We investigate quantum state discrimination with confidentiality. $N$ observers share a given quantum state belonging to a finite set of known states. The observers want to determine the state as accurately as possible and send a…
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.…
Deterministic discrimination of nonorthogonal states is forbidden by quantum measurement theory. However, if we do not want to succeed all the time, i.e. allow for inconclusive outcomes to occur, then unambiguous discrimination becomes…
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…