User contributions for Gianfranco

05:09, 10 November 2022 diff hist +4,013‎ N Store:QLMes12 ‎ Created page with "===6.4. Mental realism=== Since very beginning of quantum mechanics, noncommutativity of operators <math>\widehat{A},\widehat{B} </math> representing observables <math>A,B </math> was considered as the mathematical representation of their incompatibility. In philosophic terms, this situation is treated as impossibility of the realistic description. In cognitive science, this means that there exist mental states such that an individual cannot assign the definite values..." current
05:09, 10 November 2022 diff hist +4,013‎ N Store:QLMde12 ‎ Created page with "===6.4. Mental realism=== Since very beginning of quantum mechanics, noncommutativity of operators <math>\widehat{A},\widehat{B} </math> representing observables <math>A,B </math> was considered as the mathematical representation of their incompatibility. In philosophic terms, this situation is treated as impossibility of the realistic description. In cognitive science, this means that there exist mental states such that an individual cannot assign the definite values..."
05:09, 10 November 2022 diff hist +4,013‎ N Store:QLMfr12 ‎ Created page with "===6.4. Mental realism=== Since very beginning of quantum mechanics, noncommutativity of operators <math>\widehat{A},\widehat{B} </math> representing observables <math>A,B </math> was considered as the mathematical representation of their incompatibility. In philosophic terms, this situation is treated as impossibility of the realistic description. In cognitive science, this means that there exist mental states such that an individual cannot assign the definite values..."
05:08, 10 November 2022 diff hist +4,013‎ N Store:QLMit12 ‎ Created page with "===6.4. Mental realism=== Since very beginning of quantum mechanics, noncommutativity of operators <math>\widehat{A},\widehat{B} </math> representing observables <math>A,B </math> was considered as the mathematical representation of their incompatibility. In philosophic terms, this situation is treated as impossibility of the realistic description. In cognitive science, this means that there exist mental states such that an individual cannot assign the definite values..."
05:08, 10 November 2022 diff hist +4,013‎ N Store:QLMen12 ‎ Created page with "===6.4. Mental realism=== Since very beginning of quantum mechanics, noncommutativity of operators <math>\widehat{A},\widehat{B} </math> representing observables <math>A,B </math> was considered as the mathematical representation of their incompatibility. In philosophic terms, this situation is treated as impossibility of the realistic description. In cognitive science, this means that there exist mental states such that an individual cannot assign the definite values..."
05:07, 10 November 2022 diff hist +3,125‎ N Store:QLMes11 ‎ Created page with "===6.2. Response replicability effect for sequential questioning=== The approach based on identification of the order effect with noncommutative representation of questions (Wang and Busemeyer, 2013) was criticized in paper (Khrennikov et al., 2014). To discuss this paper, we recall the notion of ''response replicability.'' Suppose that a person, say John, is asked some question <math>A</math> and suppose that he replies, e.g, “yes”. If immediately after this, he is..." current
05:07, 10 November 2022 diff hist +3,125‎ N Store:QLMde11 ‎ Created page with "===6.2. Response replicability effect for sequential questioning=== The approach based on identification of the order effect with noncommutative representation of questions (Wang and Busemeyer, 2013) was criticized in paper (Khrennikov et al., 2014). To discuss this paper, we recall the notion of ''response replicability.'' Suppose that a person, say John, is asked some question <math>A</math> and suppose that he replies, e.g, “yes”. If immediately after this, he is..."
05:07, 10 November 2022 diff hist +3,125‎ N Store:QLMfr11 ‎ Created page with "===6.2. Response replicability effect for sequential questioning=== The approach based on identification of the order effect with noncommutative representation of questions (Wang and Busemeyer, 2013) was criticized in paper (Khrennikov et al., 2014). To discuss this paper, we recall the notion of ''response replicability.'' Suppose that a person, say John, is asked some question <math>A</math> and suppose that he replies, e.g, “yes”. If immediately after this, he is..."
05:06, 10 November 2022 diff hist +3,124‎ N Store:QLMit11 ‎ Created page with "===6.2. Response replicability effect for sequential questioning=== The approach based on identification of the order effect with noncommutative representation of questions (Wang and Busemeyer, 2013) was criticized in paper (Khrennikov et al., 2014). To discuss this paper, we recall the notion of ''response replicability.'' Suppose that a person, say John, is asked some question <math>A</math> and suppose that he replies, e.g, “yes”. If immediately after this, he is..."
05:06, 10 November 2022 diff hist +3,125‎ N Store:QLMen11 ‎ Created page with "===6.2. Response replicability effect for sequential questioning=== The approach based on identification of the order effect with noncommutative representation of questions (Wang and Busemeyer, 2013) was criticized in paper (Khrennikov et al., 2014). To discuss this paper, we recall the notion of ''response replicability.'' Suppose that a person, say John, is asked some question <math>A</math> and suppose that he replies, e.g, “yes”. If immediately after this, he is..."
05:02, 10 November 2022 diff hist −15,920‎ Quantum-like modeling in biology with open quantum systems and instruments - en ‎
05:02, 10 November 2022 diff hist +3,005‎ N Store:QLMes10 ‎ Created page with "==5. Modeling of the process of sensation–perception within indirect measurement scheme== Foundations of theory of ''unconscious inference'' for the formation of visual impressions were set in 19th century by H. von Helmholtz. Although von Helmholtz studied mainly visual sensation–perception, he also applied his theory for other senses up to culmination in theory of social unconscious inference. By von Helmholtz here are two stages of the cognitive process, and they..." current
05:02, 10 November 2022 diff hist +3,005‎ N Store:QLMde10 ‎ Created page with "==5. Modeling of the process of sensation–perception within indirect measurement scheme== Foundations of theory of ''unconscious inference'' for the formation of visual impressions were set in 19th century by H. von Helmholtz. Although von Helmholtz studied mainly visual sensation–perception, he also applied his theory for other senses up to culmination in theory of social unconscious inference. By von Helmholtz here are two stages of the cognitive process, and they..."
05:01, 10 November 2022 diff hist +3,005‎ N Store:QLMfr10 ‎ Created page with "==5. Modeling of the process of sensation–perception within indirect measurement scheme== Foundations of theory of ''unconscious inference'' for the formation of visual impressions were set in 19th century by H. von Helmholtz. Although von Helmholtz studied mainly visual sensation–perception, he also applied his theory for other senses up to culmination in theory of social unconscious inference. By von Helmholtz here are two stages of the cognitive process, and they..."
05:01, 10 November 2022 diff hist +3,005‎ N Store:QLMit10 ‎ Created page with "==5. Modeling of the process of sensation–perception within indirect measurement scheme== Foundations of theory of ''unconscious inference'' for the formation of visual impressions were set in 19th century by H. von Helmholtz. Although von Helmholtz studied mainly visual sensation–perception, he also applied his theory for other senses up to culmination in theory of social unconscious inference. By von Helmholtz here are two stages of the cognitive process, and they..."
05:01, 10 November 2022 diff hist +3,005‎ N Store:QLMen10 ‎ Created page with "==5. Modeling of the process of sensation–perception within indirect measurement scheme== Foundations of theory of ''unconscious inference'' for the formation of visual impressions were set in 19th century by H. von Helmholtz. Although von Helmholtz studied mainly visual sensation–perception, he also applied his theory for other senses up to culmination in theory of social unconscious inference. By von Helmholtz here are two stages of the cognitive process, and they..."
05:00, 10 November 2022 diff hist +3,499‎ N Store:QLMes09 ‎ Created page with "==4. Quantum instruments from the scheme of indirect measurements== The basic model for construction of quantum instruments is based on the scheme of indirect measurements. This scheme formalizes the following situation: measurement’s outputs are generated via interaction of a system <math>S</math> with a measurement apparatus <math>M</math> . This apparatus consists of a complex physical device interacting with <math>S</math> and a pointer that shows the result of me..." current
05:00, 10 November 2022 diff hist +3,499‎ N Store:QLMde09 ‎ Created page with "==4. Quantum instruments from the scheme of indirect measurements== The basic model for construction of quantum instruments is based on the scheme of indirect measurements. This scheme formalizes the following situation: measurement’s outputs are generated via interaction of a system <math>S</math> with a measurement apparatus <math>M</math> . This apparatus consists of a complex physical device interacting with <math>S</math> and a pointer that shows the result of me..."
04:59, 10 November 2022 diff hist +3,499‎ N Store:QLMit09 ‎ Created page with "==4. Quantum instruments from the scheme of indirect measurements== The basic model for construction of quantum instruments is based on the scheme of indirect measurements. This scheme formalizes the following situation: measurement’s outputs are generated via interaction of a system <math>S</math> with a measurement apparatus <math>M</math> . This apparatus consists of a complex physical device interacting with <math>S</math> and a pointer that shows the result of me..."
04:59, 10 November 2022 diff hist +3,386‎ N Store:QLMes08 ‎ Created page with "===3.4. General theory (Davies–Lewis–Ozawa)=== Finally, we formulate the general notion of quantum instrument. A superoperator acting in <math display="inline">\mathcal{L}(\mathcal{H})</math> is called positive if it maps the set of positive semi-definite operators into itself. We remark that, for each '''<math>x,\Im_A(x)</math>''' given by (13) can be considered as linear positive map. Generally any map<math>x\rightarrow\Im_A(x)</math> , where for each <m..." current
04:59, 10 November 2022 diff hist +3,386‎ N Store:QLMde08 ‎ Created page with "===3.4. General theory (Davies–Lewis–Ozawa)=== Finally, we formulate the general notion of quantum instrument. A superoperator acting in <math display="inline">\mathcal{L}(\mathcal{H})</math> is called positive if it maps the set of positive semi-definite operators into itself. We remark that, for each '''<math>x,\Im_A(x)</math>''' given by (13) can be considered as linear positive map. Generally any map<math>x\rightarrow\Im_A(x)</math> , where for each <m..."
04:59, 10 November 2022 diff hist +3,386‎ N Store:QLMfr08 ‎ Created page with "===3.4. General theory (Davies–Lewis–Ozawa)=== Finally, we formulate the general notion of quantum instrument. A superoperator acting in <math display="inline">\mathcal{L}(\mathcal{H})</math> is called positive if it maps the set of positive semi-definite operators into itself. We remark that, for each '''<math>x,\Im_A(x)</math>''' given by (13) can be considered as linear positive map. Generally any map<math>x\rightarrow\Im_A(x)</math> , where for each <m..."
04:58, 10 November 2022 diff hist +3,386‎ N Store:QLMit08 ‎ Created page with "===3.4. General theory (Davies–Lewis–Ozawa)=== Finally, we formulate the general notion of quantum instrument. A superoperator acting in <math display="inline">\mathcal{L}(\mathcal{H})</math> is called positive if it maps the set of positive semi-definite operators into itself. We remark that, for each '''<math>x,\Im_A(x)</math>''' given by (13) can be considered as linear positive map. Generally any map<math>x\rightarrow\Im_A(x)</math> , where for each <m..."
04:58, 10 November 2022 diff hist +3,499‎ N Store:QLMen09 ‎ Created page with "==4. Quantum instruments from the scheme of indirect measurements== The basic model for construction of quantum instruments is based on the scheme of indirect measurements. This scheme formalizes the following situation: measurement’s outputs are generated via interaction of a system <math>S</math> with a measurement apparatus <math>M</math> . This apparatus consists of a complex physical device interacting with <math>S</math> and a pointer that shows the result of me..."
04:58, 10 November 2022 diff hist +3,386‎ N Store:QLMen08 ‎ Created page with "===3.4. General theory (Davies–Lewis–Ozawa)=== Finally, we formulate the general notion of quantum instrument. A superoperator acting in <math display="inline">\mathcal{L}(\mathcal{H})</math> is called positive if it maps the set of positive semi-definite operators into itself. We remark that, for each '''<math>x,\Im_A(x)</math>''' given by (13) can be considered as linear positive map. Generally any map<math>x\rightarrow\Im_A(x)</math> , where for each <m..."
04:56, 10 November 2022 diff hist +6,101‎ N Store:QLMes07 ‎ Created page with "===3.3. Non-projective state update: atomic instruments=== In general, the statistical properties of any measurement are characterized by # the output probability distribution <math display="inline">Pr\{\text{x}=x\parallel\rho\}</math>, the probability distribution of the output <math display="inline">x</math> of the measurement in the input state <math display="inline">\rho </math>; # the quantum state reduction <math display="inline">\rho\rightarrow\rho_{(X=x)} </ma..." current
04:56, 10 November 2022 diff hist +6,101‎ N Store:QLMde07 ‎ Created page with "===3.3. Non-projective state update: atomic instruments=== In general, the statistical properties of any measurement are characterized by # the output probability distribution <math display="inline">Pr\{\text{x}=x\parallel\rho\}</math>, the probability distribution of the output <math display="inline">x</math> of the measurement in the input state <math display="inline">\rho </math>; # the quantum state reduction <math display="inline">\rho\rightarrow\rho_{(X=x)} </ma..."
04:55, 10 November 2022 diff hist +6,101‎ N Store:QLMfr07 ‎ Created page with "===3.3. Non-projective state update: atomic instruments=== In general, the statistical properties of any measurement are characterized by # the output probability distribution <math display="inline">Pr\{\text{x}=x\parallel\rho\}</math>, the probability distribution of the output <math display="inline">x</math> of the measurement in the input state <math display="inline">\rho </math>; # the quantum state reduction <math display="inline">\rho\rightarrow\rho_{(X=x)} </ma..."
04:55, 10 November 2022 diff hist +6,101‎ N Store:QLMit07 ‎ Created page with "===3.3. Non-projective state update: atomic instruments=== In general, the statistical properties of any measurement are characterized by # the output probability distribution <math display="inline">Pr\{\text{x}=x\parallel\rho\}</math>, the probability distribution of the output <math display="inline">x</math> of the measurement in the input state <math display="inline">\rho </math>; # the quantum state reduction <math display="inline">\rho\rightarrow\rho_{(X=x)} </ma..."
04:55, 10 November 2022 diff hist +6,101‎ N Store:QLMen07 ‎ Created page with "===3.3. Non-projective state update: atomic instruments=== In general, the statistical properties of any measurement are characterized by # the output probability distribution <math display="inline">Pr\{\text{x}=x\parallel\rho\}</math>, the probability distribution of the output <math display="inline">x</math> of the measurement in the input state <math display="inline">\rho </math>; # the quantum state reduction <math display="inline">\rho\rightarrow\rho_{(X=x)} </ma..."
15:51, 9 November 2022 diff hist −24,999‎ Quantum-like modeling in biology with open quantum systems and instruments - en ‎
15:51, 9 November 2022 diff hist +2,517‎ N Store:QLMes06 ‎ Created page with "===3.2. Von Neumann formalism for quantum observables=== In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</..." current
15:51, 9 November 2022 diff hist +2,517‎ N Store:QLMde06 ‎ Created page with "===3.2. Von Neumann formalism for quantum observables=== In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</..."
15:50, 9 November 2022 diff hist +2,517‎ N Store:QLMfr06 ‎ Created page with "===3.2. Von Neumann formalism for quantum observables=== In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</..."
15:50, 9 November 2022 diff hist +2,517‎ N Store:QLMit06 ‎ Created page with "===3.2. Von Neumann formalism for quantum observables=== In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</..."
15:50, 9 November 2022 diff hist +2,517‎ N Store:QLMen06 ‎ Created page with "===3.2. Von Neumann formalism for quantum observables=== In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</..."
15:49, 9 November 2022 diff hist +2,520‎ N Store:QLMes05 ‎ Created page with "==3. Quantum instruments== ===3.1. A few words about the quantum formalism=== Denote by <math display="inline">\mathcal{H}</math> a complex Hilbert space. For simplicity, we assume that it is finite dimensional. Pure states of a system <math>S</math> are given by normalized vectors of <math display="inline">\mathcal{H}</math> and mixed states by density operators (positive semi-definite operators with unit trace). The space of density operators is denoted by <math>S..." current
15:49, 9 November 2022 diff hist +2,520‎ N Store:QLMfr05 ‎ Created page with "==3. Quantum instruments== ===3.1. A few words about the quantum formalism=== Denote by <math display="inline">\mathcal{H}</math> a complex Hilbert space. For simplicity, we assume that it is finite dimensional. Pure states of a system <math>S</math> are given by normalized vectors of <math display="inline">\mathcal{H}</math> and mixed states by density operators (positive semi-definite operators with unit trace). The space of density operators is denoted by <math>S..."
15:49, 9 November 2022 diff hist +2,520‎ N Store:QLMde05 ‎ Created page with "==3. Quantum instruments== ===3.1. A few words about the quantum formalism=== Denote by <math display="inline">\mathcal{H}</math> a complex Hilbert space. For simplicity, we assume that it is finite dimensional. Pure states of a system <math>S</math> are given by normalized vectors of <math display="inline">\mathcal{H}</math> and mixed states by density operators (positive semi-definite operators with unit trace). The space of density operators is denoted by <math>S..."
15:49, 9 November 2022 diff hist +2,520‎ N Store:QLMit05 ‎ Created page with "==3. Quantum instruments== ===3.1. A few words about the quantum formalism=== Denote by <math display="inline">\mathcal{H}</math> a complex Hilbert space. For simplicity, we assume that it is finite dimensional. Pure states of a system <math>S</math> are given by normalized vectors of <math display="inline">\mathcal{H}</math> and mixed states by density operators (positive semi-definite operators with unit trace). The space of density operators is denoted by <math>S..."
15:48, 9 November 2022 diff hist +2,520‎ N Store:QLMen05 ‎ Created page with "==3. Quantum instruments== ===3.1. A few words about the quantum formalism=== Denote by <math display="inline">\mathcal{H}</math> a complex Hilbert space. For simplicity, we assume that it is finite dimensional. Pure states of a system <math>S</math> are given by normalized vectors of <math display="inline">\mathcal{H}</math> and mixed states by density operators (positive semi-definite operators with unit trace). The space of density operators is denoted by <math>S..."
15:48, 9 November 2022 diff hist +3,463‎ N Store:QLMes04 ‎ Created page with "==2. Classical versus quantum probability== CP was mathematically formalized by Kolmogorov (1933)<ref name=":2" /> This is the calculus of probability measures, where a non-negative weight <math>p(A)</math> is assigned to any event <math>A</math>. The main property of CP is its additivity: if two events <math>O_1, O_2</math> are disjoint, then the probability of disjunction of these events equals to the sum of probabilities: {| width="80%" | |- | width="33%" | ..." current
15:47, 9 November 2022 diff hist +3,465‎ N Store:QLMde04 ‎ Created page with "==2. Classical versus quantum probability== CP was mathematically formalized by Kolmogorov (1933)<ref name=":2" /> This is the calculus of probability measures, where a non-negative weight <math>p(A)</math> is assigned to any event <math>A</math>. The main property of CP is its additivity: if two events <math>O_1, O_2</math> are disjoint, then the probability of disjunction of these events equals to the sum of probabilities: {| width="80%" | |- | width="33%" | ..."
15:47, 9 November 2022 diff hist +3,463‎ N Store:QLMit04 ‎ Created page with "==2. Classical versus quantum probability== CP was mathematically formalized by Kolmogorov (1933)<ref name=":2" /> This is the calculus of probability measures, where a non-negative weight <math>p(A)</math> is assigned to any event <math>A</math>. The main property of CP is its additivity: if two events <math>O_1, O_2</math> are disjoint, then the probability of disjunction of these events equals to the sum of probabilities: {| width="80%" | |- | width="33%" | ..."
15:47, 9 November 2022 diff hist +3,463‎ N Store:QLMen04 ‎ Created page with "==2. Classical versus quantum probability== CP was mathematically formalized by Kolmogorov (1933)<ref name=":2" /> This is the calculus of probability measures, where a non-negative weight <math>p(A)</math> is assigned to any event <math>A</math>. The main property of CP is its additivity: if two events <math>O_1, O_2</math> are disjoint, then the probability of disjunction of these events equals to the sum of probabilities: {| width="80%" | |- | width="33%" | ..."
15:46, 9 November 2022 diff hist +6,737‎ N Store:QLMes03 ‎ Created page with "===Observations=== In textbooks on quantum mechanics, it is commonly pointed out that the main distinguishing feature of quantum theory is the presence of ''incompatible observables.'' We recall that two observables <math>A</math> <math>B</math> and are incompatible if it is impossible to assign values to them jointly. In the probabilistic model, this leads to impossibility to determine their joint probability distribution (JPD). The basic examples of incompatible obse..." current
15:46, 9 November 2022 diff hist +6,737‎ N Store:QLMde03 ‎ Created page with "===Observations=== In textbooks on quantum mechanics, it is commonly pointed out that the main distinguishing feature of quantum theory is the presence of ''incompatible observables.'' We recall that two observables <math>A</math> <math>B</math> and are incompatible if it is impossible to assign values to them jointly. In the probabilistic model, this leads to impossibility to determine their joint probability distribution (JPD). The basic examples of incompatible obse..."
15:46, 9 November 2022 diff hist +6,737‎ N Store:QLMfr03 ‎ Created page with "===Observations=== In textbooks on quantum mechanics, it is commonly pointed out that the main distinguishing feature of quantum theory is the presence of ''incompatible observables.'' We recall that two observables <math>A</math> <math>B</math> and are incompatible if it is impossible to assign values to them jointly. In the probabilistic model, this leads to impossibility to determine their joint probability distribution (JPD). The basic examples of incompatible obse..."
15:46, 9 November 2022 diff hist +6,737‎ N Store:QLMit03 ‎ Created page with "===Observations=== In textbooks on quantum mechanics, it is commonly pointed out that the main distinguishing feature of quantum theory is the presence of ''incompatible observables.'' We recall that two observables <math>A</math> <math>B</math> and are incompatible if it is impossible to assign values to them jointly. In the probabilistic model, this leads to impossibility to determine their joint probability distribution (JPD). The basic examples of incompatible obse..."
15:46, 9 November 2022 diff hist +6,737‎ N Store:QLMen03 ‎ Created page with "===Observations=== In textbooks on quantum mechanics, it is commonly pointed out that the main distinguishing feature of quantum theory is the presence of ''incompatible observables.'' We recall that two observables <math>A</math> <math>B</math> and are incompatible if it is impossible to assign values to them jointly. In the probabilistic model, this leads to impossibility to determine their joint probability distribution (JPD). The basic examples of incompatible obse..."