scholarly journals Simple communication complexity separation from quantum state antidistinguishability

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Vojtěch Havlíček ◽  
Jonathan Barrett
Keyword(s):  
Quantum State ◽  
Communication Complexity

scholarly journals Quantum Entanglement and Communication Complexity

1997 ◽  
Vol 4 (40) ◽  
Author(s):  
Harry Buhrman ◽  
Richard Cleve ◽  
Wim Van Dam
Keyword(s):  
Quantum Entanglement ◽  
Quantum State ◽  
Communication Channel ◽  
Communication Complexity ◽  
Complexity Problem

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles<br />in an entangled quantum state. We show that, although a prior<br />quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in<br />some cases. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables them to learn the value of the<br />function with only three bits of communication occurring among the parties, whereas, without quantum entanglement, four bits of communication are necessary. We also show that, for a particular two-party probabilistic communication complexity problem, quantum entanglement<br />results in less communication than is required with only classical<br />random correlations (instead of quantum entanglement). These results are a noteworthy contrast to the well-known fact that quantum entanglement cannot be used to actually simulate communication among<br />remote parties.

scholarly journals Communication complexity and the reality of the wave function

2015 ◽  
Vol 30 (01) ◽  
pp. 1530001 ◽  
Author(s):  
Alberto Montina
Keyword(s):  
Quantum State ◽  
Communication Complexity ◽  
Quantum Communication ◽  
Communication Process ◽  
Minimal Amount ◽  
Quantum Processes ◽  
Independence Property ◽  
Classical Communication ◽  
Asymptotic Equipartition Property ◽  
Quantum Communication Complexity

In this review, we discuss a relation between quantum communication complexity and a long-standing debate in quantum foundation concerning the interpretation of the quantum state. Is the quantum state a physical element of reality as originally interpreted by Schrödinger? Or is it an abstract mathematical object containing statistical information about the outcome of measurements as interpreted by Born? Although these questions sound philosophical and pointless, they can be made precise in the framework of what we call classical theories of quantum processes, which are a reword of quantum phenomena in the language of classical probability theory. In 2012, Pusey, Barrett and Rudolph (PBR) proved, under an assumption of preparation independence, a theorem supporting the original interpretation of Schrödinger in the classical framework. The PBR theorem has attracted considerable interest revitalizing the debate and motivating other proofs with alternative hypotheses. Recently, we showed that these questions are related to a practical problem in quantum communication complexity, namely, quantifying the minimal amount of classical communication required in the classical simulation of a two-party quantum communication process. In particular, we argued that the statement of the PBR theorem can be proved if the classical communication cost of simulating the communication of n qubits grows more than exponentially in n. Our argument is based on an assumption that we call probability equipartition property. This property is somehow weaker than the preparation independence property used in the PBR theorem, as the former can be justified by the latter and the asymptotic equipartition property of independent stochastic sources. The probability equipartition property is a general and natural hypothesis that can be assumed even if the preparation independence hypothesis is dropped. In this review, we further develop our argument into the form of a theorem.

scholarly journals QUANTUM KOLMOGOROV COMPLEXITY AND ITS APPLICATIONS

2007 ◽  
Vol 05 (05) ◽  
pp. 729-750 ◽  
Author(s):  
CATERINA E. MORA ◽  
HANS J. BRIEGEL ◽  
BARBARA KRAUS
Keyword(s):  
Quantum Computation ◽  
Quantum State ◽  
Kolmogorov Complexity ◽  
Communication Complexity ◽  
Quantum States ◽  
Qubit State ◽  
Binary String ◽  
Classical Communication ◽  
Pure Quantum State ◽  
Definition Of

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore, we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

Probability and Explanation

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Causal Explanation ◽  
Born Rule ◽  
Correct Application

We can use quantum theory to explain an enormous variety of phenomena by showing why they were to be expected and what they depend on. These explanations of probabilistic phenomena involve applications of the Born rule: to accept quantum theory is to let relevant Born probabilities guide one’s credences about presently inaccessible events. We use quantum theory to explain a probabilistic phenomenon by showing how its probabilities follow from a correct application of the Born rule, thereby exhibiting the phenomenon’s dependence on the quantum state to be assigned in circumstances of that type. This is not a causal explanation since a probabilistic phenomenon is not constituted by events that may manifest it: but each of those events does depend causally on events that actually occur in those circumstances. Born probabilities are objective and sui generis, but not all Born probabilities are chances.

Sign in / Sign up

Export Citation Format

Share Document