Multicopy programmable discriminators between two unknown qudit states with group-theoretic approach

2012 ◽  
Vol 12 (11&12) ◽  
pp. 1017-1033
Author(s):  
Tao Zhou ◽  
Jing Xin Cui ◽  
Xiaohua Wu ◽  
Gui Lu Long
Keyword(s):  
Theoretic Approach ◽  
Data Systems ◽  
Mixed States ◽  
Minimum Error ◽  
Unambiguous Discrimination ◽  
State Discrimination ◽  
Jordan Basis ◽  
Orthogonal Measurement ◽  
The Mean ◽  
Programmable Discriminator

The discrimination between two unknown states can be performed by a universal programmable discriminator, where the copies of the two possible states are stored in two program systems respectively and the copies of data, which we want to confirm, are provided in the data system. In the present paper, we propose a group-theretic approach to the multi-copy programmable state discrimination problem. By equivalence of unknown pure states to known mixed states and with the representation theory of $U(n)$ group, we construct the Jordan basis to derive the analytical results for both the optimal unambiguous discrimination and minimum-error discrimination. The POVM operators for unambiguous discrimination and orthogonal measurement operators for minimum-error discrimination are obtained. We find that the optimal failure probability and minimum-error probability for the discrimination between the mean input mixd states are dependent on the dimension of the unknown qudit states. We applied the approach to generalize the results of He and Bergou (2007) from qubit to qudit case, and we further solve the problem of programmable dicriminators with arbitrary copies of unknown states in both program and data systems.

scholarly journals Optimal Unambiguous Discrimination And Quantum Nonlocality Without Entanglement: Locking And Unlocking By Post-Measurement Information

2021 ◽  
Author(s):  
Donghoon Ha ◽  
Jeong San Kim
Keyword(s):  
Quantum Nonlocality ◽  
Measurement Information ◽  
Minimum Error ◽  
Separable States ◽  
Unambiguous Discrimination ◽  
State Discrimination

Abstract The phenomenon of nonlocality without entanglement(NLWE) arises in discriminating multi-party quantum separable states. Recently, it has been found that the post-measurement information about the prepared subensemble can lock or unlock NLWE in minimum-error discrimination of non-orthogonal separable states. Thus it is natrual to ask whether the availability of the post-measurement information can influence on the occurrence of NLWE even in other state-discrimination stratigies. Here, we show that the post-measurement information can be used to lock as well as unlock the occurence of NLWE in terms of optimal nambiguous discrimination. Our results can provide a useful application for hiding or sharing information based on non-orthogonal separable states.

scholarly journals Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1583
Author(s):  
Jaehee Shin ◽  
Donghoon Ha ◽  
Younghun Kwon
Keyword(s):  
Prior Probability ◽  
The State ◽  
Mixed States ◽  
Minimum Error ◽  
Prior Probabilities ◽  
Quantum Properties ◽  
State Discrimination ◽  
The Given ◽  
Qubit States ◽  
Selection Of

Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal pure states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two mixed states.

scholarly journals Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Donghoon Ha ◽  
Jeong San Kim
Keyword(s):  
Quantum State ◽  
Quantum States ◽  
Quantum Nonlocality ◽  
Quantum State Discrimination ◽  
Classical Communication ◽  
Minimum Error ◽  
Prior Probabilities ◽  
Separable States ◽  
Unambiguous Discrimination ◽  
State Discrimination

AbstractNonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.

scholarly journals Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1422
Author(s):  
Min Namkung ◽  
Younghun Kwon
Keyword(s):  
Quantum Information ◽  
Quantum State ◽  
Quantum Key Distribution ◽  
Key Distribution ◽  
Quantum States ◽  
Quantum State Discrimination ◽  
Mixed States ◽  
Generalized Measurement ◽  
Unambiguous Discrimination ◽  
State Discrimination

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.

Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions

1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Stability Criterion ◽  
Feedback Gain ◽  
Continuous Systems ◽  
Mean Square ◽  
Data Systems ◽  
Sampled Data ◽  
Input Output ◽  
Output Stability ◽  
Lumped Parameter ◽  
The Mean

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.

Minimum guesswork discrimination between quantum states

2015 ◽  
Vol 15 (9&10) ◽  
pp. 737-758
Author(s):  
Weien Chen ◽  
Yongzhi Cao ◽  
Hanpin Wang ◽  
Yuan Feng
Keyword(s):  
Error Probability ◽  
Sufficient Conditions ◽  
Optimization Criterion ◽  
Quantum States ◽  
Actual State ◽  
Information Theoretic ◽  
Minimum Error ◽  
State Discrimination ◽  
Semidefinite Programming Problem ◽  
Necessary And Sufficient

Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able to use a brute-force strategy to query the state, discrimination measurement with minimum error probability does not necessarily minimize the number of queries to get the actual state. In light of this, we take Massey's guesswork as the underlying optimization criterion and study the problem of minimum guesswork discrimination. We show that this problem can be reduced to a semidefinite programming problem. Necessary and sufficient conditions when a measurement achieves minimum guesswork are presented. We also reveal the relation between minimum guesswork and minimum error probability. We show that the two criteria generally disagree with each other, except for the special case with two states. Both upper and lower information-theoretic bounds on minimum guesswork are given. For geometrically uniform quantum states, we provide sufficient conditions when a measurement achieves minimum guesswork. Moreover, we give the necessary and sufficient condition under which making no measurement at all would be the optimal strategy.

scholarly journals TI-RADS Diagnostic Performance: Which Algorithm Is Superior and How Elastography and 4D Vascularity Improve the Malignancy Risk Assessment

Diagnostics ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 180
Author(s):  
Andreea Borlea ◽  
Florin Borcan ◽  
Ioan Sporea ◽  
Cristina Dehelean ◽  
Romeo Negrea ◽  
...  
Keyword(s):  
Risk Assessment ◽  
Histopathological Examination ◽  
Risk Estimation ◽  
Color Doppler ◽  
Strain Ratio ◽  
Point Of View ◽  
Data Systems ◽  
Statistical Point ◽  
Malignancy Risk ◽  
The Mean

Given the increased prevalence of thyroid nodules in the general population (~50%), the real challenge resides in correctly recognizing the suspicious ones. This study proposes to compare four important Thyroid Imaging and Reporting Data Systems (TI-RADS) and evaluate the contribution of elastography and 4D Color Doppler assessment of vascularity in estimating the risk of malignancy. In the study, 133 nodules with histopathological examination were included. Of these, 35 (26.31%) proved to be malignant. All nodules were classified using the four selected systems and our proposed improved score. The American College of Radiology (ACR) and EU TI-RADS had good sensitivity (94.28%, 97.14%) and NPV (93.33%, 95.83%), but fairly poor specificity (31.81%, 23.46%) and PPV (35.48%, 31.19%), with an accuracy of 42.8% and 45.8%, respectively. Horvath TI-RADS had better accuracy of 66.9% and somewhat improved specificity (62.24%), but poorer sensitivity (80%). Russ’ French TI-RADS includes elastography in the risk assessment strategy. This classification proved superior in all aspects (Se: 91.42%, Sp:82.65%, NPV:96.42%, PPV:65.30%, and Acc of 84.96%). The mean strain ratio (SR) value for malignant lesions was 5.56, while the mean SR value for benign ones was significantly lower, 2.54 (p < 0.05). It also correlated well with the response variable: histopathological result (p < 0.001). Although, adding 4D vascularity to the French score generated a similar calculated accuracy and from a statistical point of view, the parameter itself proved beneficial for predicting the malignancy risk (p < 0.001) and may add important knowledge in uncertain situations. Advanced ultrasound techniques definitely improved the risk estimation and should be used more extensively.

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