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05:21, 10 November 2022 Gianfranco talk contribs created page Store:QLMfr17 (Created page with "==11. Compound biosystems== ===11.1. Entanglement of information states of biosystems=== The state space <math>{\mathcal{H}}</math> of the biosystem <math>S</math> consisting of the subsystems <math>S_j,j=1,2,....n</math>, is the tensor product of subsystems’ state spaces<math>{\mathcal{H}}_j</math> , so {| width="80%" | |- | width="33%" |'''<big>*</big>''' | width="33%" |<math>\Im=\Im_1\otimes....\otimes\Im_n</math> | width="33%" align="right" |<math>(31)</math>...")
05:21, 10 November 2022 Gianfranco talk contribs created page Store:QLMit17 (Created page with "==11. Compound biosystems== ===11.1. Entanglement of information states of biosystems=== The state space <math>{\mathcal{H}}</math> of the biosystem <math>S</math> consisting of the subsystems <math>S_j,j=1,2,....n</math>, is the tensor product of subsystems’ state spaces<math>{\mathcal{H}}_j</math> , so {| width="80%" | |- | width="33%" |'''<big>*</big>''' | width="33%" |<math>\Im=\Im_1\otimes....\otimes\Im_n</math> | width="33%" align="right" |<math>(31)</math>...")
05:21, 10 November 2022 Gianfranco talk contribs created page Store:QLMen17 (Created page with "==11. Compound biosystems== ===11.1. Entanglement of information states of biosystems=== The state space <math>{\mathcal{H}}</math> of the biosystem <math>S</math> consisting of the subsystems <math>S_j,j=1,2,....n</math>, is the tensor product of subsystems’ state spaces<math>{\mathcal{H}}_j</math> , so {| width="80%" | |- | width="33%" |'''<big>*</big>''' | width="33%" |<math>\Im=\Im_1\otimes....\otimes\Im_n</math> | width="33%" align="right" |<math>(31)</math>...")
05:19, 10 November 2022 Gianfranco talk contribs created page Store:QLMes16 (Created page with "==9. Epigenetic evolution within theory of open quantum systems== In paper (Asano et al., 2012b), a general model of the epigenetic evolution unifying neo-Darwinian with neo-Lamarckian approaches was created in the framework of theory of open quantum systems. The process of evolution is represented in the form of ''adaptive dynamics'' given by the quantum(-like) master equation describing the dynamics of the information state of epigenome in the process of interaction wi...")
05:19, 10 November 2022 Gianfranco talk contribs created page Store:QLMde16 (Created page with "==9. Epigenetic evolution within theory of open quantum systems== In paper (Asano et al., 2012b), a general model of the epigenetic evolution unifying neo-Darwinian with neo-Lamarckian approaches was created in the framework of theory of open quantum systems. The process of evolution is represented in the form of ''adaptive dynamics'' given by the quantum(-like) master equation describing the dynamics of the information state of epigenome in the process of interaction wi...")
05:19, 10 November 2022 Gianfranco talk contribs created page Store:QLMfr16 (Created page with "==9. Epigenetic evolution within theory of open quantum systems== In paper (Asano et al., 2012b), a general model of the epigenetic evolution unifying neo-Darwinian with neo-Lamarckian approaches was created in the framework of theory of open quantum systems. The process of evolution is represented in the form of ''adaptive dynamics'' given by the quantum(-like) master equation describing the dynamics of the information state of epigenome in the process of interaction wi...")
05:19, 10 November 2022 Gianfranco talk contribs created page Store:QLMit16 (Created page with "==9. Epigenetic evolution within theory of open quantum systems== In paper (Asano et al., 2012b), a general model of the epigenetic evolution unifying neo-Darwinian with neo-Lamarckian approaches was created in the framework of theory of open quantum systems. The process of evolution is represented in the form of ''adaptive dynamics'' given by the quantum(-like) master equation describing the dynamics of the information state of epigenome in the process of interaction wi...")
05:18, 10 November 2022 Gianfranco talk contribs created page Store:QLMen16 (Created page with "==9. Epigenetic evolution within theory of open quantum systems== In paper (Asano et al., 2012b), a general model of the epigenetic evolution unifying neo-Darwinian with neo-Lamarckian approaches was created in the framework of theory of open quantum systems. The process of evolution is represented in the form of ''adaptive dynamics'' given by the quantum(-like) master equation describing the dynamics of the information state of epigenome in the process of interaction wi...")
05:16, 10 November 2022 Gianfranco talk contribs created page Store:QLMes15 (Created page with "===8.3. Operation of biological functions through decoherence=== To make the previous considerations concrete, let us consider a pure quantum state as the initial state. Suppose that a biological function <math>F</math> is dichotomous, <math>F=0,1 </math>, and it is symbolically represented by the Hermitian operator that is diagonal in orthonormal basis <math>|0\rangle</math>,<math>|1\rangle</math> . (We consider the two dimensional state space — the qubit space.) Le...")
05:16, 10 November 2022 Gianfranco talk contribs created page Store:QLMde15 (Created page with "===8.3. Operation of biological functions through decoherence=== To make the previous considerations concrete, let us consider a pure quantum state as the initial state. Suppose that a biological function <math>F</math> is dichotomous, <math>F=0,1 </math>, and it is symbolically represented by the Hermitian operator that is diagonal in orthonormal basis <math>|0\rangle</math>,<math>|1\rangle</math> . (We consider the two dimensional state space — the qubit space.) Le...")
05:16, 10 November 2022 Gianfranco talk contribs created page Store:QLMfr15 (Created page with "===8.3. Operation of biological functions through decoherence=== To make the previous considerations concrete, let us consider a pure quantum state as the initial state. Suppose that a biological function <math>F</math> is dichotomous, <math>F=0,1 </math>, and it is symbolically represented by the Hermitian operator that is diagonal in orthonormal basis <math>|0\rangle</math>,<math>|1\rangle</math> . (We consider the two dimensional state space — the qubit space.) Le...")
05:15, 10 November 2022 Gianfranco talk contribs created page Store:QLMit15 (Created page with "===8.3. Operation of biological functions through decoherence=== To make the previous considerations concrete, let us consider a pure quantum state as the initial state. Suppose that a biological function <math>F</math> is dichotomous, <math>F=0,1 </math>, and it is symbolically represented by the Hermitian operator that is diagonal in orthonormal basis <math>|0\rangle</math>,<math>|1\rangle</math> . (We consider the two dimensional state space — the qubit space.) Le...")
05:15, 10 November 2022 Gianfranco talk contribs created page Store:QLMen15 (Created page with "===8.3. Operation of biological functions through decoherence=== To make the previous considerations concrete, let us consider a pure quantum state as the initial state. Suppose that a biological function <math>F</math> is dichotomous, <math>F=0,1 </math>, and it is symbolically represented by the Hermitian operator that is diagonal in orthonormal basis <math>|0\rangle</math>,<math>|1\rangle</math> . (We consider the two dimensional state space — the qubit space.) Le...")
05:14, 10 November 2022 Gianfranco talk contribs created page Store:QLMes14 (Created page with "===8.2. Biological functions in the quantum Markov framework=== We turn to the open system dynamics with the GKSL-equation. In our modeling, Hamiltonian <math>\widehat{\mathcal{H}}</math> and Lindbladian <math>\widehat{{L}}</math> represent some special ''biological function'' <math>F</math> (see Khrennikov et al., 2018) for details. Its functioning results from interaction of internal and external information flows. In Sections 10, 11.3, <math>F</math> is some ''...")
05:14, 10 November 2022 Gianfranco talk contribs created page Store:QLMde14 (Created page with "===8.2. Biological functions in the quantum Markov framework=== We turn to the open system dynamics with the GKSL-equation. In our modeling, Hamiltonian <math>\widehat{\mathcal{H}}</math> and Lindbladian <math>\widehat{{L}}</math> represent some special ''biological function'' <math>F</math> (see Khrennikov et al., 2018) for details. Its functioning results from interaction of internal and external information flows. In Sections 10, 11.3, <math>F</math> is some ''...")
05:14, 10 November 2022 Gianfranco talk contribs created page Store:QLMfr14 (Created page with "===8.2. Biological functions in the quantum Markov framework=== We turn to the open system dynamics with the GKSL-equation. In our modeling, Hamiltonian <math>\widehat{\mathcal{H}}</math> and Lindbladian <math>\widehat{{L}}</math> represent some special ''biological function'' <math>F</math> (see Khrennikov et al., 2018) for details. Its functioning results from interaction of internal and external information flows. In Sections 10, 11.3, <math>F</math> is some ''...")
05:13, 10 November 2022 Gianfranco talk contribs created page Store:QLMit14 (Created page with "===8.2. Biological functions in the quantum Markov framework=== We turn to the open system dynamics with the GKSL-equation. In our modeling, Hamiltonian <math>\widehat{\mathcal{H}}</math> and Lindbladian <math>\widehat{{L}}</math> represent some special ''biological function'' <math>F</math> (see Khrennikov et al., 2018) for details. Its functioning results from interaction of internal and external information flows. In Sections 10, 11.3, <math>F</math> is some ''...")
05:13, 10 November 2022 Gianfranco talk contribs created page Store:QLMen14 (Created page with "===8.2. Biological functions in the quantum Markov framework=== We turn to the open system dynamics with the GKSL-equation. In our modeling, Hamiltonian <math>\widehat{\mathcal{H}}</math> and Lindbladian <math>\widehat{{L}}</math> represent some special ''biological function'' <math>F</math> (see Khrennikov et al., 2018) for details. Its functioning results from interaction of internal and external information flows. In Sections 10, 11.3, <math>F</math> is some ''...")
05:12, 10 November 2022 Gianfranco talk contribs created page Store:QLMfr13 (Created page with "==8. Open quantum systems: interaction of a biosystem with its environment== As was already emphasized, any biosystem <math>S</math> is fundamentally open. Hence, dynamics of its state has to be modeled via an interaction with surrounding environment <math> \varepsilon</math>. The states of <math>S</math> and <math> \varepsilon</math> are represented in the Hilbert spaces <math>\mathcal{H}</math> and <math>\mathcal{H}</math>. The compound system <math>S+\varepsilon</...")
05:12, 10 November 2022 Gianfranco talk contribs created page Store:QLMde13 (Created page with "==8. Open quantum systems: interaction of a biosystem with its environment== As was already emphasized, any biosystem <math>S</math> is fundamentally open. Hence, dynamics of its state has to be modeled via an interaction with surrounding environment <math> \varepsilon</math>. The states of <math>S</math> and <math> \varepsilon</math> are represented in the Hilbert spaces <math>\mathcal{H}</math> and <math>\mathcal{H}</math>. The compound system <math>S+\varepsilon</...")
05:11, 10 November 2022 Gianfranco talk contribs created page Store:QLMit13 (Created page with "==8. Open quantum systems: interaction of a biosystem with its environment== As was already emphasized, any biosystem <math>S</math> is fundamentally open. Hence, dynamics of its state has to be modeled via an interaction with surrounding environment <math> \varepsilon</math>. The states of <math>S</math> and <math> \varepsilon</math> are represented in the Hilbert spaces <math>\mathcal{H}</math> and <math>\mathcal{H}</math>. The compound system <math>S+\varepsilon</...")
05:11, 10 November 2022 Gianfranco talk contribs created page Store:QLMen13 (Created page with "==8. Open quantum systems: interaction of a biosystem with its environment== As was already emphasized, any biosystem <math>S</math> is fundamentally open. Hence, dynamics of its state has to be modeled via an interaction with surrounding environment <math> \varepsilon</math>. The states of <math>S</math> and <math> \varepsilon</math> are represented in the Hilbert spaces <math>\mathcal{H}</math> and <math>\mathcal{H}</math>. The compound system <math>S+\varepsilon</...")
05:11, 10 November 2022 Gianfranco talk contribs created page Store:QLMes13 (Created page with "==8. Open quantum systems: interaction of a biosystem with its environment== As was already emphasized, any biosystem <math>S</math> is fundamentally open. Hence, dynamics of its state has to be modeled via an interaction with surrounding environment <math> \varepsilon</math>. The states of <math>S</math> and <math> \varepsilon</math> are represented in the Hilbert spaces <math>\mathcal{H}</math> and <math>\mathcal{H}</math>. The compound system <math>S+\varepsilon</...")
05:09, 10 November 2022 Gianfranco talk contribs created page 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...")
05:09, 10 November 2022 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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...")
05:07, 10 November 2022 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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...")
05:02, 10 November 2022 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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...")
05:00, 10 November 2022 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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...")
04:59, 10 November 2022 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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...")
04:56, 10 November 2022 Gianfranco talk contribs created page 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 Gianfranco talk contribs created page 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...")

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