Advantage of Quantum Theory over Nonclassical Models of Communication

Saha, Sutapa; Bhattacharya, Some Sankar; Guha, Tamal; Halder, Saronath; Banik, Manik

doi:10.1002/andp.202000334

Cited by 13 publications

(5 citation statements)

References 54 publications

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“…We, however, conjecture that the no-go statement of Theorem 2 holds true for any such intermediate composite models. The study, made in [39], supports our conjecture where it has been shown that the intermediate compositions for the square-bit model (i.e., Ω 4 ) cannot perfectly compute the equality problem, i.e., the computation (F ≡ ∨, f ≡ ⊕) ∈ DCLC(2).…”

Section: Note That Unlikesupporting

confidence: 75%

“…For an explicit example, (F ≡ ∨, f ≡ ⊕) is a nontrivial computation that can be perfectly done in quantum theory, where ∨ denotes logical inclusive disjunction (OR) operation. This particular computation can also be thought as equality problem that asks whether x = y or not [39]. On the other hand, (F ≡ ⊕, f ≡ ∨) is also a nontrivial computation, but it cannot be done perfectly in quantum theory.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Computing Model: Classical vs. Quantum vs. Post-Quantum

Saha¹,

Guha²,

Bhattacharya³

et al. 2020

Preprint

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Computation refers to an algorithmic process of producing outputs from a given set of inputs. We consider a particular model of computation where the computing device is comprised of several components/ports placed at different spacetime locations -the inputs are distributed among different ports, whereas the output is to be assessed by some other port. Importantly, communications among the different ports are limited as the physical systems allowed to be transmitted among the different ports are constrained with information theoretic restrictions. Interestingly, this limited communication distributed computing prototype provides an efficient modus operandi to compare the computational strength of different mathematical models used to describe those physical systems. We come up with computing tasks where quantum theory outperforms its classical counterpart. More surprisingly, a broader class of operational theories with state or/and effect space structures more exotic than quantum theory turns out to be suboptimal in performing some distributed computing tasks. We characterize the computations that can be perfectly accomplished in quantum theory but not in other theories. The proposed computing model thus provides a new approach to single out quantum theory in the theory space and promises a novel perspective towards the axiomatic derivation of Hilbert space quantum mechanics.

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Section: Note That Unlikesupporting

confidence: 75%

Section: Resultsmentioning

confidence: 99%

Distributed Computing Model: Classical vs. Quantum vs. Post-Quantum

Saha¹,

Guha²,

Bhattacharya³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Even gon different non-classical aspects of these models which in turn provide better understandings of the Hilbert space structure of quantum theory [81][82][83][84][85][86]. Here we study these models to explore their communication utility while playing the Restaurant games.…”

Section: Odd Gonmentioning

confidence: 99%

Classical analogue of quantum superdense coding and communication advantage of a single quantum

Patra¹,

Naik²,

Lobo³

et al. 2022

Preprint

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We analyze the communication utility of a single quantum system when the sender and receiver share neither any entanglement nor any classical shared randomness. To this aim, we propose a class of two-party communication games that cannot be won with a noiseless 1-bit classical channel, whereas the goal can be perfectly achieved if the channel is assisted by classical shared randomness. This resembles an advantage similar to the quantum superdense coding phenomenon where preshared entanglement can enhance communication utility of a perfect quantum communication line. Quite surprisingly, we show that a qubit communication without any assistance of classical shared randomness can achieve the goal, and hence establishes a novel quantum advantage in the simplest communication scenario. In pursuit of a deeper origin of this advantage we show that an advantageous quantum strategy must invoke quantum interference both at the encoding step by the sender and at the decoding step by the receiver. A subclass of these games can be won deterministically if the sender communicates some non-classical toy systems described by symmetric polygonal state spaces. We then proceed to design a variant of the game that can be won neither with 1-bit communication nor with a polygon system, but 1-qubit communication yields a perfect strategy, establishing a strict quantum nature of the advantage. To this end, we show that the quantum advantages are robust against imperfect encodings-decodings, making the protocols implementable with presently available quantum technologies.

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“…For a detailed overview of this framework we refer to the works [9][10][11][12][13][14]. In the recent past several interesting results have been reported within this framework [25][26][27][28][29][30][31]. A GPT is specified by a list of system types and the composition rules specifying combination of several systems, where a system S is specified by identifying the three-tuple (Ω S , E S , T S ) of the state space, effect space, and the set of transformations.…”

Section: A Framework Of Gptmentioning

confidence: 99%

Timelike correlations and quantum tensor product structure

Sen¹,

Lobo²,

Patra³

et al. 2022

Preprint

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The state space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with local quantum description. For instance, unentangled Gleason's theorem allows a state space that includes density operators as a proper subset among all possible composite states. However, bipartite correlations obtained in Bell type experiments from this broader state space are in-fact quantum simulable, and hence such spacelike correlations are no good to make distinction among different compositions. In this work we analyze communication utilities of these different composite models and show that they can lead to distinct utilities in a simple communication game involving two players. Our analysis, thus, establishes that beyond quantum composite structure can lead to beyond quantum correlations in timelike scenario and hence welcomes new principles to isolate the quantum correlations from the beyond quantum ones. We also prove a no-go that the classical information carrying capacity of different such compositions cannot be more than the corresponding quantum composite systems.

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Advantage of Quantum Theory over Nonclassical Models of Communication

Cited by 13 publications

References 54 publications

Distributed Computing Model: Classical vs. Quantum vs. Post-Quantum

Distributed Computing Model: Classical vs. Quantum vs. Post-Quantum

Classical analogue of quantum superdense coding and communication advantage of a single quantum

Timelike correlations and quantum tensor product structure

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