Quantum communication and complexity

In the setting of communication complexity, two distributed parties want to compute a function depending on both their inputs, using as little communication as possible. The required communication can sometimes be significantly lowered if we allow the parties the use of quantum communication. We survey the main results of the young area of quantum communication complexity; its relation to teleportation and dense coding, the main examples of fast quantum communication protocols, lower bounds, and some applications.

[1]  Gilles Brassard.  Quantum communication complexity: a survey , 2004, Proceedings. 34th International Symposium on Multiple-Valued Logic.

[2]  Andris Ambainis,et al.  Dense quantum coding and a lower bound for 1-way quantum automata , 1998, STOC '99.

[3]  Ronald de Wolf,et al.  Communication complexity lower bounds by polynomials , 1999, Proceedings 16th Annual IEEE Conference on Computational Complexity.

[4]  Ronald de Wolf,et al.  Bounds for small-error and zero-error quantum algorithms , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[5]  Andrew Chi-Chih Yao,et al.  Probabilistic computations: Toward a unified measure of complexity , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[6]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[7]  Andrew Chi-Chih Yao,et al.  Quantum Circuit Complexity , 1993, FOCS.

[8]  Ashwin Nayak,et al.  On communication over an entanglement-assisted quantum channel , 2002, STOC '02.

[9]  D. Deutsch.  Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  Harry Buhrman,et al.  Quantum Computing and Communication Complexity , 2001, Bull. EATCS.

[11]  Juraj Hromkovic,et al.  Communication Complexity and Parallel Computing , 1997, Texts in Theoretical Computer Science An EATCS Series.

[12]  Andris Ambainis,et al.  The quantum communication complexity of sampling , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[13]  A. Holevo.  Bounds for the quantity of information transmitted by a quantum communication channel , 1973 .

[14]  Alain Tapp,et al.  Quantum Entanglement and the Communication Complexity of the Inner Product Function , 1998, QCQC.

[15]  Ran Raz,et al.  Exponential separation of quantum and classical communication complexity , 1999, STOC '99.

[16]  Peter W. Shor,et al.  Quantum Information Theory , 1998, IEEE Trans. Inf. Theory.

[17]  Kurt Mehlhorn,et al.  Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract) , 1982, STOC '82.

[18]  M. Sipser,et al.  Limit on the Speed of Quantum Computation in Determining Parity , 1998, quant-ph/9802045.

[19]  Bala Kalyanasundaram,et al.  The Probabilistic Communication Complexity of Set Intersection , 1992, SIAM J. Discret. Math..

[20]  Hartmut Klauck.  On rounds in quantum communication , 2000 .

[21]  Alexander A. Razborov,et al.  On the Distributional Complexity of Disjointness , 1992, Theor. Comput. Sci..

[22]  Amnon Ta-Shma,et al.  Classical versus quantum communication complexity , 1999, SIGA.

[23]  Ronald de Wolf,et al.  On Quantum Versions of the Yao Principle , 2001, STACS.

[24]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  Peter Hoyer,et al.  Multiparty quantum communication complexity. , 1997 .

[26]  Hartmut Klauck,et al.  Lower bounds for quantum communication complexity , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[27]  Peter Frankl,et al.  Complexity classes in communication complexity theory , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[28]  Avi Wigderson,et al.  Quantum vs. classical communication and computation , 1998, STOC '98.

[29]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[30]  R. Cleve,et al.  SUBSTITUTING QUANTUM ENTANGLEMENT FOR COMMUNICATION , 1997, quant-ph/9704026.

[31]  Srinivasan Venkatesh,et al.  Lower Bounds in the Quantum Cell Probe Model , 2001, ICALP.

[32]  Hartmut Klauck,et al.  On quantum and probabilistic communication: Las Vegas and one-way protocols , 2000, STOC '00.

[33]  Ashwin Nayak,et al.  Optimal lower bounds for quantum automata and random access codes , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[34]  A. Razborov.  Quantum communication complexity of symmetric predicates , 2002, quant-ph/0204025.

[35]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[36]  E. Kushilevitz,et al.  Communication Complexity: Basics , 1996 .

[37]  Lo,et al.  Unconditional security of quantum key distribution over arbitrarily long distances , 1999, Science.

[38]  Gilles Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

[39]  Ronald de Wolf,et al.  Quantum lower bounds by polynomials , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[40]  Ilan Newman,et al.  Public vs. private coin flips in one round communication games (extended abstract) , 1996, STOC '96.

[41]  Gilles Brassard,et al.  Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..

[42]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[43]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[44]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[45]  Dave Bacon,et al.  Classical simulation of quantum entanglement without local hidden variables , 2001 .

[46]  Harry Buhrman,et al.  Quantum Entanglement and Communication Complexity , 2000, SIAM J. Comput..

[47]  Hartmut Klauck,et al.  Quantum Communication Complexity , 2022 .

[48]  László Babai,et al.  Randomized simultaneous messages: solution of a problem of Yao in communication complexity , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[49]  R. de Wolf,et al.  Characterization of non-deterministic quantum query and quantum communication complexity , 2000, Proceedings 15th Annual IEEE Conference on Computational Complexity.

[50]  Hartmut Klauck,et al.  Interaction in quantum communication and the complexity of set disjointness , 2001, STOC '01.

[51]  Umesh V. Vazirani,et al.  Quantum Complexity Theory , 1997, SIAM J. Comput..

[52]  Andrew M. Steane,et al.  Physicists triumph at 'Guess My Number' , 2000 .

[53]  Ronald de Wolf,et al.  Improved Quantum Communication Complexity Bounds for Disjointness and Equality , 2001, STACS.

[54]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[55]  Ashwin Nayak,et al.  Interaction in Quantum Communication Complexity , 2000, ArXiv.

[56]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[57]  Gilles Brassard,et al.  Cost of Exactly Simulating Quantum Entanglement with Classical Communication , 1999 .

[58]  R. Mcweeny.  On the Einstein-Podolsky-Rosen Paradox , 2000 .

[59]  Christof Zalka.  GROVER'S QUANTUM SEARCHING ALGORITHM IS OPTIMAL , 1997, quant-ph/9711070.

[60]  Ilan Newman,et al.  Private vs. Common Random Bits in Communication Complexity , 1991, Inf. Process. Lett..

[61]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.