Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Computer Engineering and Applications Journal

Discrimination of quantum operation

Jing Zhang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Authors consider the perfect discrimination problem by applying the method of unambiguous discrimination quantum states to quantum operation,and get a necessary and sufficient condition for quantum operation;second authors extend set dis-crimination of quantum states to set discrimination of quantum operation,at the same time,obtain two necessary and sufficient conditions for quantum operation;at last,authors consider the lower bounds of the quantum operation.

Related papers

Unambiguous discrimination among quantum operations

Guoming Wang, Mingsheng Ying

We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses, respectively. For the latter case we explicitly construct the input states and corresponding measurements that accomplish the task. It is also found that the introduction of entanglement can improve the discrimination.

arXiv:quant-ph/0512142•Physical Review A•Apr 3, 2006•109 citations

Unambiguous discrimination between quantum operations

Guoming Wang, Mingsheng Ying

We address the problem of unambiguous discrimination between a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses respectively. For the latter case we explicitly construct the input states and corresponding measurements that accomplish the task. It is found that the introduction of entanglement can improve the discrimination. The advantage of our strategy over minimum-error discrimination is also discussed.

•Dec 18, 2005•2 citations

Optimum Unambiguous Discrimination of Quantum States Based on Semidefinite Programming

Guohua Dong

For the general problem of optimum unambiguous discrimination of quantum states, it is very hard to get the explicit analytical form for optimum detection operators. Therefore, it is necessary to find an efficient numerical method for designing optimum detection operators. According to the theory of semidefinite programming, it is demonstrated that the design of the optimal quantum measurement can be formulated as a standard semidefinite programming problem, and the optimality conditions for semidefinite programming can be used to perspicuously derive a set of optimality conditions for optimum detection operators.By means of the standard semidefinite programming, the maximum value of the success probability of detection and the optimum detection operators can be obtained directly in polynomial time. It is exemplified that this method is simple to be implemented and can be used to design optimum detection operators for quantum-state discrimination efficiently.

Jisuanji fangzhen•Jan 1, 2008•0 citations

On the feasibility conditions of quantum state discrimination

Chung-Chin Lu, Shiuan-Hao Kuo

In this paper, we consider the quantum unambiguous discrimination problem of a set of linearly independent pure states. With a constructive procedure, we establish a necessary and sufficient condition for feasible POVM measurements for unambiguous quantum state discrimination. We develop methods to calculate the optimal discrimination efficiencies for minimizing the inconclusive probability and the optimal discrimination efficiencies for the minimax criterion. Finally, we prove a necessary and sufficient condition to have a feasible POVM measurement which achieves the minimum inconclusive probability criterion and the minimax criterion simultaneously and show that geometrically uniform states with equal a priori probabilities meet this condition.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2017•0 citations

Unambiguous discrimination between mixed quantum states

Yuan Feng, Runyao Duan, Mingsheng Ying

We prove that the states secretly chosen from a mixed state set can be perfectly discriminated if and only if they are orthogonal. The sufficient and necessary condition under which nonorthogonal mixed quantum states can be unambiguously discriminated is also presented. Furthermore, we derive a series of lower bounds on the inconclusive probability of unambiguous discrimination of states from a mixed state set with a priori probabilities.

arXiv:quant-ph/0403147•Physical Review A•Jul 14, 2004•93 citations

Discrimination of mixed quantum states: Reversible maps and unambiguous strategies

Matthias Kleinmann

The discrimination of two mixed quantum states is a fundamental task in quantum state estimation and quantum information theory. In quantum state discrimination a quantum system is assumed to be in one of two possible – in general mixed – non-orthogonal quantum states. The discrimination then consists of a measurement strategy that allows to decide in which state the system was before the measurement. In unambiguous state discrimination the aim is to make this decision without errors, but it is allowed to give an inconclusive answer. Especially interesting are measurement strategies that minimize the probability of an inconclusive answer. A starting point for the analysis of this optimization problem was a result by Eldar et al. [Phys. Rev. A 69, 062318 (2004)], which provides non-operational necessary and sufficient conditions for a given measurement strategy to be optimal. These conditions are reconsidered and simplified in such a way that they become operational. The simplified conditions are the basis for further central results: It is shown that the optimal measurement strategy is unique, a statement that is e.g. of importance for the complexity analysis of optimal measurement devices. The optimal measurement strategy is derived for the case, where one of the possible input states has at most rank two, which was an open problem for many years. Furthermore, using the optimality criterion it is shown that there always exists a threshold probability for each state, such that below this probability it is optimal to exclude this state from the discrimination strategy. If the two states subject to discrimination can be brought to a diagonal structure with (2×2)-dimensional blocks, then the unambiguous discrimination of these states can be reduced to the unambiguous discrimination of pure states. A criterion is presented that allows to identify the presence of such a structure for two self-adjoint operators. This criterion consists of the evaluation of three commutators and allows an explicit construction of the (2×2)-dimensional blocks. As an important application of unambiguous state discrimination, unambiguous state comparison, i.e., the question whether two states are identical or not, is generalized and optimal measurements for this problem are constructed. If for a certain family of states, a physical device maps the input state to an output state, such that a second device can be built that yields back the original input state, such a map is called reversible on this family. With respect to state discrimination, such reversible maps are particularly interesting, if the output states are pure. A complete characterization of all families that allow such a reversible and purifying map is provided. If the states are mapped to pure states, but the map itself is not reversible, upper and lower bounds are analyzed for the “deviation from perfect faithfulness”, a quantity which measures the deviation from a reversible mapping.

•Jan 1, 2008•0 citations
Authors consider the perfect discrimination problem by applying the method of unambiguous discrimination quantum states to quantum operation,and get a necessary and sufficient condition for quantum operation;second authors extend set dis-crimination of quantum states to set discrimination of quantum operation,at the same time,obtain two necessary and sufficient conditions for quantum operation;at last,authors consider the lower bounds of the quantum operation.
We address the problem of unambiguous discrimination between a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses respectively. For the latter case we explicitly construct the input states and corresponding measurements that accomplish the task. It is found that the introduction of entanglement can improve the discrimination. The advantage of our strategy over minimum-error discrimination is also discussed.
For the general problem of optimum unambiguous discrimination of quantum states, it is very hard to get the explicit analytical form for optimum detection operators. Therefore, it is necessary to find an efficient numerical method for designing optimum detection operators. According to the theory of semidefinite programming, it is demonstrated that the design of the optimal quantum measurement can be formulated as a standard semidefinite programming problem, and the optimality conditions for semidefinite programming can be used to perspicuously derive a set of optimality conditions for optimum detection operators.By means of the standard semidefinite programming, the maximum value of the success probability of detection and the optimum detection operators can be obtained directly in polynomial time. It is exemplified that this method is simple to be implemented and can be used to design optimum detection operators for quantum-state discrimination efficiently.
In this paper, we consider the quantum unambiguous discrimination problem of a set of linearly independent pure states. With a constructive procedure, we establish a necessary and sufficient condition for feasible POVM measurements for unambiguous quantum state discrimination. We develop methods to calculate the optimal discrimination efficiencies for minimizing the inconclusive probability and the optimal discrimination efficiencies for the minimax criterion. Finally, we prove a necessary and sufficient condition to have a feasible POVM measurement which achieves the minimum inconclusive probability criterion and the minimax criterion simultaneously and show that geometrically uniform states with equal a priori probabilities meet this condition.
The discrimination of two mixed quantum states is a fundamental task in quantum state estimation and quantum information theory. In quantum state discrimination a quantum system is assumed to be in one of two possible – in general mixed – non-orthogonal quantum states. The discrimination then consists of a measurement strategy that allows to decide in which state the system was before the measurement. In unambiguous state discrimination the aim is to make this decision without errors, but it is allowed to give an inconclusive answer. Especially interesting are measurement strategies that minimize the probability of an inconclusive answer. A starting point for the analysis of this optimization problem was a result by Eldar et al. [Phys. Rev. A 69, 062318 (2004)], which provides non-operational necessary and sufficient conditions for a given measurement strategy to be optimal. These conditions are reconsidered and simplified in such a way that they become operational. The simplified conditions are the basis for further central results: It is shown that the optimal measurement strategy is unique, a statement that is e.g. of importance for the complexity analysis of optimal measurement devices. The optimal measurement strategy is derived for the case, where one of the possible input states has at most rank two, which was an open problem for many years. Furthermore, using the optimality criterion it is shown that there always exists a threshold probability for each state, such that below this probability it is optimal to exclude this state from the discrimination strategy. If the two states subject to discrimination can be brought to a diagonal structure with (2×2)-dimensional blocks, then the unambiguous discrimination of these states can be reduced to the unambiguous discrimination of pure states. A criterion is presented that allows to identify the presence of such a structure for two self-adjoint operators. This criterion consists of the evaluation of three commutators and allows an explicit construction of the (2×2)-dimensional blocks. As an important application of unambiguous state discrimination, unambiguous state comparison, i.e., the question whether two states are identical or not, is generalized and optimal measurements for this problem are constructed. If for a certain family of states, a physical device maps the input state to an output state, such that a second device can be built that yields back the original input state, such a map is called reversible on this family. With respect to state discrimination, such reversible maps are particularly interesting, if the output states are pure. A complete characterization of all families that allow such a reversible and purifying map is provided. If the states are mapped to pure states, but the map itself is not reversible, upper and lower bounds are analyzed for the “deviation from perfect faithfulness”, a quantity which measures the deviation from a reversible mapping.