Quantum information in base<i>n</i>defined by state partitions

We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to capture the relativity and variability of our structures with respect to the observation means, sheaves of algebras may need be introduced. We provide the general formalism based on algebras which exhibits the relativity of multipartiteness and localization. PROLEGOMENA CUM PHYSICAL MOTIVATIONThe non-local behavior of quantum systems is virtually undisputed. There is ample experimental evidence suggesting that there exist quantum states of an essentially non-local nature, an issue which is verified by the statistics of observations. Entanglement is a crucial resource for quantum information processing and quantum communication. As it turns out, while it may be easy to produce nonentangled states, it is difficult to fabricate and maintain entangled ones. Recently, multipartite entanglement has been classified by the use of partitions of the set of subsystems (Dür and Cirac, 2000).We may regard this as the first indication of the idea we wish to explore later, namely, the relativity of the 'property' for a subsystem to be observed-in effect, to be localized-somewhere. Albeit, it is perhaps inadequate to just say relativity; one should also say uncertainty of some sort, as the position itself is created at the very moment of the preparation of the state. Quanta act not only

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“…This admits an immediate generalization to quantum systems which was carried out by Svozil (2002) and Zanardi (2001). Let us briefly review it.…”

Section: Tensor Product Structures (Tpss)mentioning

confidence: 96%

Combinatory-Algebraic Perspective on Multipartiteness, Entanglement and Quantum Localization

Raptis

Zapatrin²

2005

Int J Theor Phys

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“…Relative to this single value definite proposition, all other propositions corresponding to non-orthogonal vectors are indeterminate. Zeilinger's Foundational Principle [11,12] is a corollary of this fact, once an orthonormal basis system including the vector corresponding to this determinate property is fixed: it is always possible to define filters corresponding to equipartitions of basis states which are co-measurable and resolve states corresponding to single basis elements [17,18].…”

Section: Type Of Randomnessmentioning

confidence: 99%

A Note on the Statistical Sampling Aspect of Delayed Choice Entanglement Swapping

Svozil

2018

Probing the Meaning of Quantum Mechanics

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“…functional parity: in terms of subspaces in fourdimensional Hilbert space with the basis B 2 ≡ {|e 1 , |e 2 } ≡ (1/2) 1, −1, −1, 1 T , (1/2) 1, −1, 1, −1 T , and written as spectral sum P = |e 1 e 1 | − |e 2 e 2 | corresponding to a partitioning [39][40][41]…”

Section: A Examplementioning

confidence: 99%

Orthogonal Vector Computations

Svozil

2016

Entropy

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Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.Keywords: quantum theory; probability theory; quantum logic; quantum algorithms; parity PACS: 03.65.Ca; 03.65.Aa; 03.65.Aa; 03.67.Ac Identifying Quantum Physical Means for ComputationThe hypothesis pursued in this paper is that the power of quantum computation solely resides in a proper "translation" of "holistic" properties of functions-manifesting themselves in the relational values for different elements of their domain, or of their entire image-into orthogonal subspaces and their associated perpendicular projections. This is usually facilitated by quantum parallelism-the possibility to co-represent and co-encode classically distinct and mutually exclusive clauses into simultaneous coherent superpositions thereof. However, in order to take advantage of parallelism, it is necessary to be able to analyse the resulting quantum state by suitably chosen orthogonal projections. In what follows we shall therefore attempt to enumerate conditions under which a given algorithmic task can be quantum mechanically encoded into orthogonal subspaces, thereby identifying criteria for potential quantum speedups. This paper is organized as follows: after a brief and somewhat iconoclastic exposition of the standard quantum formalism (which may be amusing to some but considered to be superfluous by others) strategies to encode properties of computable functions into orthogonal subspaces are discussed. This involves the possibility to orthogonalise non-orthogonal vectors of some initial Hilbert space by interpreting them as orthogonal projections of mutually orthogonal vectors in a Hilbert space of greater dimension. Locating Quantum ResourcesStarting with Plack's [1] (p. 31) "act of despair" it may not be totally unreasonable to state that the newly discovered quantum capacities, unheard of in classical continuum mechanics, caused shock and awe among some of the most prominent creators of quantum mechanics. Most notably Schrödinger struggled with quantum coherence, today known as quantum parallelism, throughout his entire life, bringing forward seemingly absurd consequences of the formalism, such as the cat paradox, or quantum jellification [2]. In the same series of papers [3] he also mentioned the capacity that multiple quanta may be entangled; a resource related to quantum non-locality, which was put forward by Einstein on various occasions [4,5] to question the consistency of quantum and relativity theory.On the formal side, Hilbert space quantum mechanics [6] and, in particular, quantum logic have been conceived [7] as attempts to systematically identify and study the valid, feasible, operational resources and capacities of quantized physical systems in terms of algebraic structures arising

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Quantum information in basendefined by state partitions

Cited by 20 publications

References 3 publications

Combinatory-Algebraic Perspective on Multipartiteness, Entanglement and Quantum Localization

Combinatory-Algebraic Perspective on Multipartiteness, Entanglement and Quantum Localization

A Note on the Statistical Sampling Aspect of Delayed Choice Entanglement Swapping

Orthogonal Vector Computations

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