Quaestiones disputatae de observatione Piotr Mironowicz Department of Algorithms and System Modeling, Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology National Quantum Information Centre in Gdańsk 18 czerwca 2017, Toruń Collaborative results with J.K.Korbicz, E.Aguilar, P.Ćwikliński and P.Horodecki. National Science Centre (NCN) grant 2014/14/E/ST2/00020 and the John Templeton Foundation ID 5603. Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 1 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Fundamental questions What does it mean to exist? What does it mean to exist objectively ? What does exist objectively? How does existence relate to observations? Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 2 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Protagoras (refered by Plato’s Socrates) Soc. Bravely said, boy; (...) You say that knowledge is perception? Theaet. Yes. Soc. Well, you have delivered yourself of a very important doctrine about knowledge; it is indeed the opinion of Protagoras, who has another way of expressing it, Man, he says, is the measure of all things, of the existence of things that are, and of the non-existence of things that are not :-You have read him? (...) Soc. Now is the wind, regarded not in relation to us but absolutely, cold or not; or are we to say, with Protagoras, that the wind is cold to him who is cold, and not to him who is not? (...) Soc. Then perception is always of existence , and being the same as knowledge is unerring? Theaet. Clearly. [Plato, Theaetetus 151e-152c, transl. Benjamin Jowett] Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 3 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Plato and Aristotle Plato: only Ideas (Forms) exist, and perceptions are just stimuli for recollection of the knowledge. Forms exist on their own. Aristotle ( Hylomorphism ): the existing objects (substances) are constituted by both unperceived matter and perceivable form. Forms exist in real things. Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 4 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Berkeley and Kant Berkeley: Esse est percipi , to be is to be perceived (by spirits, i.e. conscious subjects or observers). Since the perception is relative, there exist sensations , but there is no real things . God has to be the source of sensations. [Berkeley, Three Dialogues between Hylas and Philonous (1713)] Kant distinguished the unintelligible but existing things-in-itself, noumenon , and things that appear, phenomenon , perceived by a reason via senses of a particular being. [Kant, Critique of Pure Reason (1781)] Other important statements: 19th century positivism; Husserl and phenomenology. Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 5 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Epistemic intuition The philosophers differ greatly in their views on the relation between observations and existence. Protagoras: observation = ⇒ existence Plato: observation ≪ existence Aristotle: observation � existence Berkeley: observation ≡ existence Kant: observation ⊥ existence positivism: OBSERVATION existence Husserl: observation Common epistemic intuition: the objectively existing things should not be perceived in contradictory ways by different observers . Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 6 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Inter-subjectivity of perceptions Suitable notion of objectivity of perceptions: A state of the system S is objective if many observers can find out (and agree on) the state of S independently, and without perturbing it . [W. Żurek, Nat. Phys. 2009; R. Horodecki, J. K. Korbicz, P. Horodecki, Phys. Rev. A 2015.] More precisely: Inter-subjectivity not objectivity [Ajdukiewicz 1949]. K. Ajdukiewicz, rector of UAM Poznań, 1948-1952. Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 7 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Quantum inter-subjectivity Question: What information can being broadcasted (in order to ensure objectivity) to multiple observers and how? Recall NO-GO theorems: no-cloning theorem, no-broadcast theorem! Related question: How does the classical world emerge out of quantum laws of physics? Żurek: The part of information about the quantum system which is proliferated in many copies in the environment becomes classical . Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 8 / 24 Quaestiones disputatae de observatione
Ontology and epistemology Inter-subjective perception vs. the measurement problem Question: What happens when a measurement is performed?, and Question: How (at what circumstances) a measurement is performed? the measurement problem the inter-subjective perception single device multi-party measurement agreement (possibly ontologically significant) (epistemic) Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 9 / 24 Quaestiones disputatae de observatione
Broadcasting of quantum information Spectrum Broadcast Structures Intuition: If the results of a measuring device are different, the states of the device should also be different . The state of an observed object and its observers is of the following form called a Spectrum Broadcast Structure (SBS): � � ̺ ( k ) with ̺ ( k ) ⊥ ̺ ( k ) ̺ SBS ≡ p i | i �� i | ⊗ , i i j � �� � i k system � �� � measuring devices where k denotes observers. [J. K. Korbicz, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 2014; R. Horodecki, J. K. Korbicz, P. Horodecki, Phys. Rev. A 2015] Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 10 / 24 Quaestiones disputatae de observatione
Broadcasting of quantum information Spectrum Broadcast Structures Examples of models leading to Spectrum Broadcast Structures (asymptotically in time): Illuminated sphere: J. K. Korbicz, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 112 , 120402 (2014). QBM: J. Tuziemski, J. K. Korbicz, EPL 112 , 40008 (2015); J. Tuziemski, J. K. Korbicz, Photonics 2 , 228-240 (2015); J. Tuziemski, J. K. Korbicz, J. Phys. A 49, 445301 (2016). Gravity: J. K. Korbicz, J. Tuziemski, arXiv:1612.08864. Spin-spin: P. Mironowicz, J. K. Korbicz, P. Horodecki, Phys. Rev. Lett. 118, 150501 (2017). Spin-boson: A. Lampo, J. Tuziemski, M. Lewenstein, J. K. Korbicz, arXiv:1702.08427. How Spectrum Broadcast Structures are being formed? Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 11 / 24 Quaestiones disputatae de observatione
Broadcasting of quantum information A central system with environment Quantum Setup: An observed system S , M -partite environment, ̺ ( 0 ) ≡ ̺ S ( 0 ) ⊗ � M k = 1 ̺ ( k ) ( 0 ) . d S � ⊗ � k B ( k ) . Quantum measurement limit interaction: H = a i | i �� i | i = 1 � �� � A Discarding unobserved parts of the environment: � � ̺ ( k ) ̺ Obs ( t ) = p i | i �� i | ⊗ ( t )+ i i k ∈ Obs � � � γ ( k ) ̺ ( k ) ⊗ σ ij | i �� j | ij ( t ) i , j ( t ) . i � = j k / ∈ Obs k ∈ Obs ( t ) ≡ Tr � i , j ( t ) � ̺ ( k ) i , j ( t ) ≡ U ( k ) ( t ) ̺ ( k ) ( 0 ) U ( k ) † ( t ) ; ̺ ( k ) ( t ) ≡ ̺ ( k ) i , i ( t ) ; σ ij ≡ � i | ̺ ( 0 ) | j � ; p i ≡ σ i , i ; γ ( k ) ̺ ( k ) i j i ij How far is the state from the Spectrum Broadcast Structure form? Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 12 / 24 Quaestiones disputatae de observatione
Broadcasting of quantum information How far is the state from the Spectrum Broadcast Structure form? Compare the Spectrum Broadcast Structure: � � ̺ ( k ) with ̺ ( k ) ⊥ ̺ ( k ) ̺ SBS ≡ p i | i �� i | ⊗ , i i j i k and the actual state: how close to ̺ ( k ) ( t ) ⊥ ̺ ( k ) ( t ) ? i j � �� � � � ̺ ( k ) ̺ Obs ( t ) = p i | i �� i | ⊗ ( t ) + i i k ∈ Obs � � � γ ( k ) ̺ ( k ) ⊗ σ ij | i �� j | ij ( t ) i , j ( t ) . i � = j k / ∈ Obs k ∈ Obs � �� � how close to 0? Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 13 / 24 Quaestiones disputatae de observatione
Broadcasting of quantum information Overlap (fidelity) of states � √ ρ 1 ρ 2 √ ρ 1 . Overlap of quantum states: B ( ρ 1 , ρ 2 ) ≡ Tr B ( ρ 1 , ρ 2 ) = 1 if the states are exactly the same. B ( ρ 1 , ρ 2 ) = 0 if the states are completely different. Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 14 / 24 Quaestiones disputatae de observatione
Broadcasting of quantum information The cumulative error of discrimination � � � � p i , ̺ ( k ) P ( k ) Discriminate states from ensemble using projectors . i i The cumulative error of discrimination vs. the overlap: √ p i p j B � � �� � � � � � ∀ � � ∃ � ̺ ( k ) I − P ( k ) ̺ ( k ) , ̺ ( k ) p i Tr ≤ . i i i j p i ,̺ ( k ) P ( k ) i i i i � = j � �� � probability of error of discrimination ̺ ( k ) → P ̺ ( k ) ≡ P ( k ) ̺ ( k ) P ( k ) (if successful) i i i i i ≡ Tr � � The probability of the correct guess : p ( k ) P ̺ ( k ) . i i Piotr Mironowicz (Gdańsk Univ. Tech.) 18 czerwca 2017, Toruń 15 / 24 Quaestiones disputatae de observatione
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