“Hyperbits”: The information quasiparticles

Pawłowski, Marcin; Winter, Andreas

doi:10.1103/physreva.85.022331

Cited by 34 publications

(43 citation statements)

References 13 publications

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“…To generalize this idea to an n-cube inscribed in an n-dimensional sphere, we use the intuition of hyperbits, which are a way to visualize such unit vectors in a quantum mechanical setting. A full discussion of hyperbits and their equivalence to certain quantum protocols is beyond the scope of this paper, but we refer the interested reader to the work of Pawlowski and Winter [PW12].…”

Section: A Construction Of a Quantum Po-rac N With Optimal Biasmentioning

confidence: 99%

Optimal bounds for parity-oblivious random access codes

et al. 2016

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Random access coding is an information task that has been extensively studied and found many applications in quantum information. In this scenario, Alice receives an n-bit string x, and wishes to encode x into a quantum state r x , such that Bob, when receiving the state r x , can choose any bit Î i n [ ] and recover the input bit x i with high probability. Here we study two variants: parity-oblivious random access codes (RACs), where we impose the cryptographic property that Bob cannot infer any information about the parity of any subset of bits of the input apart from the single bits x i ; and evenparity-oblivious RACs, where Bob cannot infer any information about the parity of any even-size subset of bits of the input. In this paper, we provide the optimal bounds for parity-oblivious quantum RACs and show that they are asymptotically better than the optimal classical ones. Our results provide a large non-contextuality inequality violation and resolve the main open problem in a work of Spekkens et al (2009 Phys. Rev. Lett.102 010401). Second, we provide the optimal bounds for evenparity-oblivious RACs by proving their equivalence to a non-local game and by providing tight bounds for the success probability of the non-local game via semidefinite programming. In the case of evenparity-oblivious RACs, the cryptographic property holds also in the device independent model. IntroductionQuantum information theory studies how information is encoded in quantum mechanical systems and how it can be transmitted through quantum channels. A main question is whether quantum information is more powerful than classical information. A celebrated result by Holevo [Hol73] shows that quantum information cannot be used to compress classical information. In high level, in order to transmit n uniformly random classical bits, one needs to transmit no less than n quantum bits. This might imply that quantum information is no more powerful than classical information. This however is wrong in many situations. In the model of communication complexity, one can show that transmitting quantum information may result in exponential savings on the communication needed to solve specific problems [BCWdW01, BJK04, GKK + 08, Raz99, RK11].One specific information task that has been extensively studied in quantum information is the notion of random access codes (RACs) [ANTV02, ANTV99, Nay99]. In this scenario, Alice receives an n-bit string x, drawn from the uniform distribution, and wishes to encode x into a quantum state r x , such that Bob, when receiving the state r x , can choose any bit Î i n [ ] and recover the input bit x i with high probability by performing some general quantum operation on r x .RACs have been used in various situations in quantum information and computation, including in communication complexity, non-locality, extractors and device-independent cryptography [BARdW08, DV10, INRY07, LPY + , PZ10]. Even though this task seems easier than transmitting the entire input string x, it is known that the length of quantum RACs must be ...

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Section: A Construction Of a Quantum Po-rac N With Optimal Biasmentioning

confidence: 99%

Optimal bounds for parity-oblivious random access codes

et al. 2016

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“…We introduce in this section a family of GPTs that we call hypersphere theories (HSTs). These theories have been studied before [13,16,19,[33][34][35][36][37][38]. The state space of single systems in HSTs is defined as the unit ball of dimension n, r r 1…”

Section: Hypersphere Theoriesmentioning

confidence: 99%

“…We consider a particular class of GPTs in which the state space of the communicating systems corresponds to an Euclidean ball of arbitrary dimension n .  Î These hypersphere theories (HSTs), as we call them here, have been previously investigated [13,16,19,[33][34][35][36][37][38]. They have important physical motivations.…”

Section: Introductionmentioning

confidence: 99%

Hyperdense coding and superadditivity of classical capacities in hypersphere theories

2015

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In quantum superdense coding, two parties previously sharing entanglement can communicate a two bit message by sending a single qubit. We study this feature in the broader framework of general probabilistic theories. We consider a particular class of theories in which the local state space of the communicating parties corresponds to Euclidian hyperballs of dimension n (the case n = 3 corresponds to the Bloch ball of quantum theory). We show that a single n-ball can encode at most one bit of information, independently of n. We introduce a bipartite extension of such theories for which there exist dense coding protocols such that n log 1 2 + ( ) bits are communicated if entanglement is previously shared by the communicating parties. For n 3, > these protocols are more powerful than the quantum one, because more than two bits are communicated by transmission of a system that locally encodes at most one bit. We call this phenomenon hyperdense coding (HDC). Our HDC protocols imply superadditive classical capacities: two entangled systems can encode n log 1 2 2 + > ( ) bits, even though each system individually encodes at most one bit. In our examples, HDC and superadditivity of classical capacities come at the expense of violating tomographic locality or dynamical continuous reversibility.

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“…There is a simple relation for the problem [12]: Let us consider a marginal distribution for Bob and Eve, R(i, j). Here Eve is not binary-restricted (i = 0, 1 and j = 0, 1, 2, ...).…”

Section: Maximizing Guessing Probability Pementioning

confidence: 99%

“…Indeed, a monogamy relation that is valid for no-signaling probabilities is explicitly employed to show the security. This approach can be applied even if the eavesdropper's alphabet is not binary [12,13].…”

Section: Introductionmentioning

confidence: 99%

No-signaling quantum key distribution: solution by linear programming

Hwang

Bae

Killoran

2014

Quantum Inf Process

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We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob's bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár-Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.

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“Hyperbits”: The information quasiparticles

Cited by 34 publications

References 13 publications

Optimal bounds for parity-oblivious random access codes

Optimal bounds for parity-oblivious random access codes

Hyperdense coding and superadditivity of classical capacities in hypersphere theories

No-signaling quantum key distribution: solution by linear programming

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