H. Buhrman, R. Cleve, and W. van Dam, "Quantum entanglement and communication complexity", preprint available from the LANL quant-ph archive 9705033, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Buhrman [21] introduced the variant with classical communication and shared EPR pairs, and exhibited the first quantum protocol provably better than any classical protocol. It uses quantum entanglement to save 1 bit of classical communication. This gap was extended by Buhrman, Cleve, and van Dam [16] and, for more than 2 parties, by Buhrman, van Dam, Hyer, and Tapp [19] 5.2 Buhrman, Cleve, Wigderson The first impressively large gaps between quantum and classical communication complexity were exhibited by Buhrman, Cleve, and Wigderson [17] Their protocols are distributed versions of known ....

H. Buhrman, R. Cleve, and W. van Dam. Quantum entanglement and communication complexity. quant-ph/9710054, 18 May 1997.

....effects already serve as ingredients in different computation and communication tasks. Entanglement can be used, for example, in order to gain advantage in communication. If two parties, Alice and Bob, want to communicate, they can save bits of communication if they share entangled pairs of qubits[69, 51, 70, 14]. Teleportation can be viewed as a quantum computation[49] and beautiful connections were drawn[35] between teleportation and quantum algorithms which are used to correct quantum noise. All these are uses of quantum effects in quantum computation. However, I believe that the full potential of ....

.... the following transformation on the basis states: jai 7 Gamma j Psi Q;a i = 1 p Q Q Gamma1 X b=0 e 2iab=Q jbi: 29) 40 We will first consider the special case of Q = 2 m , which is simpler than the general case, since classical techniques for fast Fourier transforms can be adopted[172, 51, 72, 80, 109] I will give here a nice description by Cleve et al. 70] Later I ll describe Kitaev s[123] more general quantum Fourier transform, for any Abelian group, which implies a beautiful alternative factorization algorithm. Quantum fast Fourier transform. Let Q = 2 m . An integer a 2 f0; 1; 2 ....

Buhrman H, Cleve R and van Dam W, Quantum Entanglement and Communication Complexity, in LANL e-print quant-ph/9705033, http://xxx.lanl.gov (1997)

No context found.

H. Buhrman, R. Cleve, and W. van Dam, "Quantum entanglement and communication complexity", preprint available from the LANL quant-ph archive 9705033, 1997.

No context found.

H. Buhrman, R. Cleve, and W. van Dam, "Quantum Entanglement and Communication Complexity", preprint available from the LANL quant-ph archive 9705033, 1997.

No context found.

H. Buhrman, R. Cleve, and W. van Dam, "Quantum Entanglement and Communication Complexity", preprint available from the LANL quant-ph archive 9705033, 1997.

No context found.

H. Buhrman, R. Cleve, and W. van Dam, "Quantum entanglement and communication complexity", preprint available from the LANL quant-ph archive 9705033, 1997.

....share this entangled state the communication problem can be solved with two bits of communication whereas without such a prior shared state three bits are necessary. That is there is a function f such that C (f) 2 whereas C(f) 3. Better separations in the multiparty setting were found in [BCvD97] and [BvDHT99] The latter paper exhibits a function f for k parties such that C (f) k and C(f) Omega Gamma k log(k) Next we will turn our attention to the qubit communication model Q(f ) However keep in mind that protocols for this model can be translated to the model where both ....

H. Buhrman, R. Cleve, and W. van Dam. Quantum entanglement and communication complexity. accepted for SIAM journal on Computing, see http://xxx.lanl.gov/abs/quant-ph/9705033, may 1997.

....protocols with independent random sources. Kremer [12] showed that, in this model, the communication complexity of IP is# (n) whenever the required correctness probability is 1 # for a constant 0 # # 1 2 (Kremer attributes the proof methodology to Yao) Cleve and Buhrman [8] see also [6]) introduced another variation of the classical communication complexity scenario that also involves quantum information, but in a di#erent way. In this model, Alice and Bob have an initial supply of particles in an entangled quantum state, such as Einstein PodolskyRosen (EPR) pairs, but the ....

H. Buhrman, R. Cleve, and W. van Dam, "Quantum Entanglement and Communication Complexity", preprint available from the LANL quant-ph archive 9705033, 1997.

....Modulo Sum Problem Given k parties, with each one real value x i . Under the assumption that we know that the x values sum up to one: P i x i = 1) we want to know if this sum is even or odd. It has been shown that this can be computed with k bits of communication in the quantum case[2, 4, 6], whereas without entanglement we need k log k bits of communication[6] 2.2 The Impossibility of the Inner Product Function Definition of the problem: For two parties who have an N bit vector x and y, what is the value of the inner product of those vectors modulo two That is, evaluate ....

Harry Buhrman, Richard Cleve and Wim van Dam, "Quantum Entanglement and Communication Complexity", Technical Report in the BRICS Research Series, no. RS-97-40 (University of Aarhus, Denmark), January 1998. Also as quant-ph report no. 9705033.

No context found.

Buhrman H, Cleve R and van Dam W, Quantum Entanglement and Communication Complexity, in LANL e-print quant-ph/9705033, http://xxx.lanl.gov (1997)

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