Quantum Advantage for Shared Randomness Generation

Guha, Tamal; Alimuddin, Mir; Rout, Sumit; Mukherjee, Amit; Bhattacharya, Some Sankar; Banik, Manik

doi:10.22331/q-2021-10-27-569

Cited by 14 publications

(5 citation statements)

References 76 publications

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“…A similar process will yield H(p)-bit of shared randomness from the state ρ = p |00 00| + (1 − p) |11 11|, with p ∈ [0, 1]. For more elaborative discussions on classical shared randomness from a resource theoretic perspective we refer to the work [32].…”

Section: Definition 3 (Classical Correlated Strategy)mentioning

confidence: 99%

“…However, it is important to note that to create classical shared randomness between two distant parties, classical communication is a necessary resource, and hence in this work we will consider it to be a costly resource. A number of works in other branches of research [27][28][29] as well as in quantum information theory [30][31][32] already exist where nontrivial utilities of classical shared randomness have been been pointed out.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Definition 3 (Classical Correlated Strategy)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Patra¹,

Naik²,

Lobo³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such a state generally allows correlation between two coins placed at the left and right compartments of the Box [41]. However, action of the mixing device M c ix on both compartments kills any such correlation and the box state becomes completely mixed, i.e.…”

Section: Appendix A: Physical Theories and Computationmentioning

confidence: 99%

Resource dependent undecidability: computability landscape of distinct Turing theories

Antony¹

2021

Preprint

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Can a problem undecidable with classical resources be decidable with quantum ones? The answer expected is no; as both being Turing theories, they should not solve the Halting problem -a problem unsolvable by any Turing machine. Yet, we provide an affirmative answer to the aforesaid question. We come up with a novel logical structure to formulate infinitely many such problems for any pair of distinct Turing theories, including but not limited to the classical and quantum theories. Importantly, a class of other decision problems, such as the Halting one, remains unsolvable in all those theories. The apparent paradoxical situation gets resolved once it is perceived that the reducibility of Halting problem changes with varying resources available for computations in different theories. In the end, we propose a multi-agent game where winnability of the player having access to only classical resources is undecidable while quantum resources provide a perfect winning strategy.

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“…It follows from the Gottesman-Knill theorem that it is possible to efficiently simulate any stabilizer circuit on a classical computer, hence rendering stabilizer states and operations useless for universal quantum computation [43,44]. For this reason, this model fits the mold of quantum resource theories where all the states and operations that cannot provide any quantum advantage are treated as free [19,24,[45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Quantifying dynamical magic with completely stabilizer preserving operations as free

Saxena,

Gour

2022

Preprint

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In this paper, we extend the resource theory of magic to the channel case by considering completely stabilizer preserving operations (CSPOs) as free. We introduce and characterize the set of CSPO preserving and completely CSPO preserving superchannels. We quantify the magic of quantum channels by extending the generalized robustness and the min relative entropy of magic from the state to the channel domain and show that they bound the single-shot dynamical magic cost and distillation. We also provide analytical conditions for qubit interconversion under CSPOs and show that it is a linear programming feasibility problem and hence can be efficiently solved. Lastly, we give a classical simulation algorithm whose runtime is related to the generalized robustness of magic for channels. Our algorithm depends on some pre-defined precision, and if there is no bound on the desired precision then it achieves a constant runtime.

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Quantum Advantage for Shared Randomness Generation

Cited by 14 publications

References 76 publications

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

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

Resource dependent undecidability: computability landscape of distinct Turing theories

Quantifying dynamical magic with completely stabilizer preserving operations as free

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