Unambiguous quantum state elimination for qubit sequences

Quantum state elimination measurements tell us what states a quantum system does not have.This is different from state discrimination, where one tries to determine what the state of a quantum system is rather than what it is not.Apart from being of fundamental interest, quantum state elimination may find uses in quantum communication and quantum cryptography.We consider unambiguous quantum state elimination for two or more qubits, where each qubit can be in one of two possible states.Optimal measurements for eliminating one and two states out of four two-qubit states are given.We also prove that if we want to maximize the average number of eliminated overall N-qubit states, then individual measurements on each qubit are optimal.Quantum state elimination measurements tell us what states a quantum system does not have.This is different from state discrimination, where one tries to determine what the state of a quantum system is rather than what it is not.Apart from being of fundamental interest, quantum state elimination may find uses in quantum communication and quantum cryptography.We consider unambiguous quantum state elimination for two or more qubits, where each qubit can be in one of two possible states.Optimal measurements for eliminating one and two states out of four two-qubit states are given.We also prove that if we want to maximize the average number of eliminated overall N-qubit states, then individual measurements on each qubit are optimal.

arXiv:2003.01800Physical Review ResearchMar 4, 20209 citations

Strictly incoherent operations for one-qubit systems

Shuanping Du, Zhaofang Bai

arXiv:2011.14602Physics Letters AFeb 6, 20210 citations

Quantum tomography via unambiguous state discrimination

Roberto Salazar, A. Delgado

We study the determination of an unknown mixed state of a $d$ -dimensional quantum system by means of unambiguous state discrimination. We show that optimal and nonoptimal unambiguous state discrimination can be used to reconstruct unknown states of a qubit. This result is extended to the case of a qudit by a sequence of reconstructions in two-dimensional subspaces. The total number of projections scales approximately as $2{d}^{2}$ for $d$ large; this is twice as much as in the case of tomography based on mutually unbiased bases or symmetric informationally complete positive-operator-valued measures, and less than the ${d}^{3}$ projections required by standard tomography.We study the determination of an unknown mixed state of a $d$-dimensional quantum system by means of unambiguous state discrimination. We show that optimal and nonoptimal unambiguous state discrimination can be used to reconstruct unknown states of a qubit. This result is extended to the case of a qudit by a sequence of reconstructions in two-dimensional subspaces. The total number of projections scales approximately as $2{d}^{2}$ for $d$ large; this is twice as much as in the case of tomography based on mutually unbiased bases or symmetric informationally complete positive-operator-valued measures, and less than the ${d}^{3}$ projections required by standard tomography.

Physical Review AJul 25, 201215 citations

A group-theoretic approach to elimination measurements of qubit sequences

Mark S. Hillery, Erika Andersson, Ittoop Vergheese Puthoor

Abstract Most measurements are designed to tell you which of several alternatives have occurred, but it is also possible to make measurements that eliminate possibilities and tell you an alternative that did not occur. Measurements of this type have proven useful in quantum foundations and in quantum cryptography. Here we show how group theory can be used to design such measurements. This requires that the set of states being considered possesses a symmetry described by a group. After some general considerations, we focus on the case of measurements on two-qubit states that eliminate one state. We then move on to construct measurements that eliminate two three-qubit states and four four-qubit states. The sets of states eliminated constitute cosets of a subgroup. A condition that constrains the construction of elimination measurements is then presented. Finally, in an appendix, we briefly consider the case of elimination measurements with failure probabilities and an elimination measurement on n-qubit states.Abstract Most measurements are designed to tell you which of several alternatives have occurred, but it is also possible to make measurements that eliminate possibilities and tell you an alternative that did not occur. Measurements of this type have proven useful in quantum foundations and in quantum cryptography. Here we show how group theory can be used to design such measurements. This requires that the set of states being considered possesses a symmetry described by a group. After some general considerations, we focus on the case of measurements on two-qubit states that eliminate one state. We then move on to construct measurements that eliminate two three-qubit states and four four-qubit states. The sets of states eliminated constitute cosets of a subgroup. A condition that constrains the construction of elimination measurements is then presented. Finally, in an appendix, we briefly consider the case of elimination measurements with failure probabilities and an elimination measurement on n-qubit states.

arXiv:2002.02055Journal of Physics A Mathematical and TheoreticalOct 7, 20250 citations

UNAMBIGUOUS STATE IDENTIFICATION APPLIED TO QUANTUM INFORMATION PROCESSING

Luis Roa, Carlos Enrique Saavedra Rubilar, Rodrigo Fuentes Inzunza

Jan 1, 20040 citations

We study the determination of an unknown mixed state of a

d

-dimensional quantum system by means of unambiguous state discrimination. We show that optimal and nonoptimal unambiguous state discrimination can be used to reconstruct unknown states of a qubit. This result is extended to the case of a qudit by a sequence of reconstructions in two-dimensional subspaces. The total number of projections scales approximately as

2{d}^{2}

for

d

large; this is twice as much as in the case of tomography based on mutually unbiased bases or symmetric informationally complete positive-operator-valued measures, and less than the

{d}^{3}

projections required by standard tomography.