Communication of partial ignorance with qubits

Heinosaari, Teiko; Kerppo, Oskari

doi:10.1088/1751-8121/ab3ae4

Cited by 23 publications

(34 citation statements)

References 17 publications

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“…The ultraweak majorization relation was first introduced in [84] as I/O degradation but in the current physical context it was only considered (and renamed) recently in [85]. The reason behind the term ultraweak matrix majorization comes from the earlier investigation into matrix majorization [86] and weak matrix majorization [87]: the previous definition reduces to that of the matrix majorization in the case when n = j and L = 1 n , and weak matrix majorization when k = m and R = 1 k .…”

Section: Ultraweak Matrix Majorizationmentioning

confidence: 99%

“…The operational interpretation of ultraweak matrix majorization is the following [85]. Let us consider a communication task that produces a communication matrix C ∈ C k,l (S) with states {s 1 , .…”

Section: Operational Interpretationmentioning

confidence: 99%

“…A natural task is to consider the minimal and maximal elements with respect to this partial order. It was shown in [85] that for a row-stochastic matrix M ∈ M row n,m we have that…”

Section: The Order Structurementioning

confidence: 99%

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Entanglement protection via periodic environment resetting in continuous-time quantum-dynamical processes

et al. 2018

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The temporal evolution of entanglement between a noisy system and an ancillary system is analyzed in the context of continuous-time open quantum system dynamics. Focusing on a couple of analytically solvable models for qubit systems, we study how Markovian and non-Markovian characteristics influence the problem, discussing in particular their associated entanglement-breaking regimes. These performances are compared with those one could achieve when the environment of the system is forced to return to its input configuration via periodic instantaneous resetting procedures.

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Section: Ultraweak Matrix Majorizationmentioning

confidence: 99%

Section: Operational Interpretationmentioning

confidence: 99%

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Entanglement protection via periodic environment resetting in continuous-time quantum-dynamical processes

et al. 2018

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“…Apart from this fundamental interest, quantum state elimination might be useful for applications in quantum information and quantum communication. Examples of this are the communication tasks in [9][10][11], and a protocol for quantum oblivious transfer [12]. In 1-out-of-2 oblivious transfer, a receiver should receive one out of two bits, with no information about the other.…”

Section: Introductionmentioning

confidence: 99%

Unambiguous quantum state elimination for qubit sequences

Crickmore

Puthoor

Ricketti

et al. 2020

Phys. Rev. Research

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Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart from being of fundamental interest, quantum state elimination may find uses in quantum communication and quantum cryptography. We consider unambiguous quantum state elimination for two or more qubits, where each qubit can be in one of two possible states. Optimal measurements for eliminating one and two states out of four two-qubit states are given. We also prove that if we want to maximise the average number of eliminated overall N -qubit states, then individual measurements on each qubit are optimal.

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“…Ref. [29] defines and studies tasks of communicating 'partial ignorance', including communication tasks using antidistinguishable quantum states that are similar to those used here.…”

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confidence: 99%

Simple communication complexity separation from quantum state antidistinguishability

Havlíček

Barrett

2020

Phys. Rev. Research

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A set of n pure quantum states is called antidististinguishable if there exists an n-outcome measurement that never outputs the outcome 'k' on the k-th quantum state. We describe sets of quantum states for which any subset of three states is antidistinguishable and use this to produce a two-player communication task that can be solved with log d qubits, but requires one-way communication of at least log(4/3)(d − 1) − 1 ≈ 0.415(d − 1) − 1 classical bits. The advantages of the approach are that the proof is simple and self-contained -not needing, for example, to rely on hard-to-establish prior results in combinatorics -and that with slight modifications, non-trivial bounds can be established in any dimension ≥ 3. The task can be framed in terms of the separated parties solving a relation, and the separation is also robust to multiplicative error in the output probabilities. We show, however, that for this particular task, the separation disappears if two-way classical communication is allowed. Finally, we state a conjecture regarding antidistinguishability of sets of states, and provide some supporting numerical evidence. If the conjecture holds, then there is a two-player communication task that can be solved with log d qubits, but requires one-way communication of Ω(d log d) classical bits.

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Communication of partial ignorance with qubits

Cited by 23 publications

References 17 publications

Entanglement protection via periodic environment resetting in continuous-time quantum-dynamical processes

Entanglement protection via periodic environment resetting in continuous-time quantum-dynamical processes

Unambiguous quantum state elimination for qubit sequences

Simple communication complexity separation from quantum state antidistinguishability

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