C.H. Bennett and S.J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states", Phys. Rev. Lett., Vol. 69, No. 20, 1992, pp. 2881--2884.  Home/Search   Document Not in Database   Summary   APS   Related Articles   Check

....of information from one party to another, or significantly reduce the classical complexity of computing functions visa vis private coin protocols [14, Section 3. 3] On the other hand, prior entanglement leads to startling phenomena such as quantum teleportation [2] and superdense coding [4]. In particular, superdense coding allows us to transmit n classical bits with perfect fidelity by sending only n 2 quantum bits. The problem of characterising the power of prior entanglement has ba#ed many researchers [7, 12] especially in the setting of bounded error protocols. It is open ....

....remains unchanged by it (see [17, Section 2.4] especially Section 2.4.3) Nonetheless, it allows us to express Bob s mixed state in a convenient form. This proves the lemma. By a simple dimensional argument, can now get an alternative proof of the fact that the superdense coding scheme of [4] is optimal (in the case of encoding without ancilla) We omit the proof. In general, we can tolerate a little error in the decoding process. This opens up the possibility of Alice being able to reduce the communication significantly. The following theorem places limits on the savings achieved. ....

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C. Bennett and S. Wiesner. Communication via oneand two-particle operators on Einstein-Podolsky-Rosen states. Physical Review Letters, 69:2881--2884, 1992.

....overviews on quantum communication complexity see [29] and [16] A slightly di erent scenario proposed in [8] and [9] allows the players to start the protocol possessing some (input independent) qubits that are entangled with those of the other player. Due to the superdense coding technique of [2] in this model 2 classical bits can be communicated by transmitting one qubit (and using up one EPR pair) See [30, 15] for some examples of lower bounds via communication complexity in the quantum setting. Unfortunately so far only few applicable lower bound methods for quantum protocols are ....

....beginning. Then they communicate according to an ordinary quantum protocol. This model can be simulated by allowing rst an arbitrary input independent communication with no cost followed by a usual quantum communication protocol in which the cost is measured. The superdense coding technique of [2] allows to transmit n bits of classical information with dn=2e qubits in this model. De nition 6 The quantum bounded error communication complexity with entanglement and error is denoted Q (f) Let Q (f) Q 1=3 (f) For surveys on quantum communication complexity see [29] and ....

C.H. Bennett, S.J. Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., vol.69, pp.2881-2884, 1992.

....A quantum computer can do this with one sixth of the queries that a classical computer requires: quantum calls versus classical calls. This also illustrates that the procedure described here is not a superdense coding in disguise , which would allow a reduction by only a factor of two[21]. 3.3 Definition of the Interrogation Problem The setting for this chapter is as follows. We try to investigate the potential differences between a quantum and a classical computer when both cases are confronted with an oracle z. The only thing known in advance about this z is that it is a ....

....we consider the n = 1 case of two distributed qubits. Take the four Bell states ( 00# 11#) # ( 00# 11#) # ( 01# 10#) 10#) As these states are mutually orthogonal, we can use the uniform source AB , to encode two bits of information. [21] It is also straightforward to see that all the partially traced out states are identical to the same totally mixed qubit: # A = # B = 0##0 I for all i. Hence, for one of the # s we must have QCor(# AB ) QC (# I# 2. This result easily generalizes to the n n qubit case ....

Charles H. Bennett and Stephen Wiesner. Communication via one- and twoparticle operators on Einstein-Podolsky-Rosen states. Physical Review Letters, 69:2881--2884, 1992.

....away from Alice [3] So EPR pairs, along with a classical communication channel, effectively constitute a quantum channel. Conversely, superdense coding is possible with EPR pairs: if Alice and Bob share an EPR pair, then Alice can transport 2 classical bits to Bob by just sending one qubit [7]. For the teleportation and dense coding to work perfectly, perfect EPR pairs are needed. Individual qubits are prone to errors, which make for imperfect pairs. This creates the need for generating perfect (or almost perfect) EPR pairs from imperfect ones. This problem of extracting EPR pairs is ....

C. H. Bennett and S. J. Wiesner, Communication via one- and two-particle operators on Einstein-PodolskyRosen states, Phys. Rev. Lett. 69, 2881 (1992).

....In a quantum protocol (as de ned in [38] the players exchange qubits rather than bits. Another scenario, where the players may also possess some (input independent) qubits that are entangled with the other players qubits is proposed in [11] and [12] Due to the superdense coding technique of [5] in this model 2 classical bits can be communicated by transmitting one qubit (and using one entangled qubit) The main objective of quantum communication complexity theory is to determine the maximum speedup one can get in comparison to classical communication for the di erent modes of ....

....set of (entangled) qubits. Then they communicate, where we consider qubit communication. This model can be simulated by allowing rst an input independent communication (to set up the entanglement) with no cost and then a communication with cost. The superdense coding technique of [5] allows to transmit n bits of information with dn=2e qubits in this model. We denote the complexity in this model by the superscript e. For the de nition of one way qfa s we refer to [24] and [28] Our results hold for the models de ned in both papers. We furthermore consider exact qfa s (no ....

C.H.Bennett, S.J.Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., vol.69, pp.2881-2884, 1992.

....complexity that has also been studied in the literature is that of communication with prior entanglement (see, e.g. 14] 12] In this model, the communicating parties may hold an arbitrary input independent entangled state in the beginning of a protocol. One can use superdense coding [15] to transmit n classical bits of information using only dn=2e qubits when entanglement is allowed. The players may also use measurements on EPR pairs to create a shared classical random key. While 5 the rst idea often decreases the communication complexity by a factor of two, the second sometimes ....

C.H. Bennett and S.J. Wiesner, \Communication via one- and two-particle operators on einstein- podolskyrosen states," Physical review letters, vol. 69, pp. 2881-2884, 1992.

....away from Alice [BBC 93] So EPR pairs, along with a classical communication channel, effectively constitute a quantum channel. Conversely, superdense coding is possible with EPR pairs: if Alice and Bob share an EPR pair, then Alice can transport 2 classical bits to Bob by just sending one qubit [BW92]. For the teleportation and dense coding to work perfectly, perfect EPR pairs are needed. Nevertheless, individual qubits are prone to errors, which may end up creating imperfect EPR pairs. These imperfect EPR pairs behave like a noisy channel qubits teleported with these EPR pairs can become ....

C. H. Bennett and S. J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phyc. Rev. Lett. 69, 2881 (1992).

....of quantum communication complexity that has also been studied in the literature is that of communication with prior entanglement (see, e.g. 8, 7] In this model, the communicating parties may hold an arbitrary inputindependent entangled state in the beginning. One can use superdense coding [4] to transmit n classical bits of information using only #n 2# qubits when entanglement is allowed. The players may also use measurements on EPR pairs to create a shared classical random key. While the first idea often decreases the communication complexity by a factor of two, the second ....

C.H. Bennett and S.J. Wiesner. Communication via one- and two-particle operators on EinsteinPodolsky -Rosen states. Physical Review Letters, 69:2881--2884, 1992.

....6 Alice still needs to send k qubits. Moreover Cleve et.al. CvDNT98] show that the same is true when both parties share EPR pairs and classical communication is used. For the third variant, where both EPR pairs and qubits are used, things are slightly different. Bennett and Wiesner [BW92] show that in this case there is a kind of a reverse of Theorem 2. This is a scheme, called super dense coding, that allows Alice to send two classical bits with one qubit to Bob provided they share an EPR pair. It can be shown that like Holevo s theorem this is optimal. We will next see that the ....

C. Bennett and S. Wiesner. Communication via one- and twoparticle operators on Einstein-Podolsky-Rosen states. Physiscal Review Letters, 69:2881--2884, 1992.

....of quantum communication complexity that has also been studied in the literature is that of communication with prior entanglement (see, e.g. 8, 7] In this model, the communicating parties may hold an arbitrary inputindependent entangled state in the beginning. One can use superdense coding [4] to transmit n classical bits of information using only dn=2e qubits when entanglement is allowed. The players may also use measurements on EPR pairs to create a shared classical random key. While the rst idea often decreases the communication complexity by a factor of two, the second sometimes ....

C.H. Bennett and S.J. Wiesner. Communication via one- and two-particle operators on EinsteinPodolsky -Rosen states. Physical Review Letters, 69:2881-2884, 1992.

....the bits to be correct. A quantum computer can do this with one sixth of the queries that a classical computer requires (N 10 versus 3N 5 calls) This also illustrates that the procedure described here is not a superdense coding in disguise which would only allow a reduction by a factor of two[2]. 2 Preliminaries The setting for this article is as follows. We try to investigate the potential di#erences between a quantum and a classical computer when both cases are confronted with an oracle #. The only thing known in advance about this # is that it is a binary valued function with a ....

C. Bennett and S. Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Physical Review Letters, 69:2881-- 2884, 1992.

....this is precisely what happens in teleportation and dense coding, and dramatically so, because without entanglement assistance teleportation, i.e. the transmission of quantum information on a classical channel, would not only be less efficient, but virtually impossible. In the original papers [BW, BB] the new possibilities were demonstrated by giving an explicit example, based on qubits. It was clear early on that extensions to systems with higher dimensional Hilbert spaces were possible, not only to powers of 2, by running the process several times, but to any dimension 2 d 1 [BB] The ....

C.H. Bennett, S.J. Wiesner, "Communication via oneand two-particle operators on Einstein-Podolsky-Rosen states", Phys.Rev.Lett. 69(1992)2881--2884

....probabilistic scenario with n = 2 where prior entanglement enables one bit of communication to be saved. 2 Bounds for Exact Qubit Protocols In this section, we consider exact qubit protocols computing IP , and prove Eq. 2) Note that the upper bound follows from so called superdense coding [4]: by sending dn=2e qubits in conjunction with dn=2e EPR pairs, Alice can transmit her n classical bits of input to Bob, enabling him to evaluate IP . For the lower bound, we consider an arbitrary exact qubit protocol that computes IP , and convert it (in two stages) to a protocol for which Theorem ....

.... simulated by a 2m bit protocol using teleportation [3] employing EPR pairs of entanglement) Also, if the communication pattern in an m bit protocol is such that an even number of bits is always sent during each party s turn then it can be simulated by an m=2 qubit protocol by superdense coding [4] (which also employs EPR pairs) However, this latter simulation technique cannot, in general, be applied directly, especially for protocols where the parties take turns sending single bits. We can nevertheless obtain a slightly weaker simulation of bit protocols by qubit protocols for IP that is ....

C.H. Bennett and S.J. Wiesner, \Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states", Phys. Rev. Lett., Vol. 69, No. 20, 1992, pp. 2881-2884.

....communication channel for classical information is helpful as we will show below. 5.1. Teleportation Astonishingly, quantum information can be transmitted by classical information when the two parties say Alice and Bob initialI 741 ly share an additional resource, a so called EPR pair (see [18, 19] for the theory and [20] for experiments) The process of teleportation is reflected by the quantum circuits shown in Fig. 1. EPR state Bell basis Bob s correction EPR state Bell basis classical data Bob s correction Figure 1: Quantum circuit for teleportation. The upper circuit transforms ....

Charles H. Bennett and Stephen J. Wiesner, "Communication via one- and two-particle operators on EinsteinPodolsky -Rosen states", Physical Review Letters, vol. 69, no. 20, pp. 2881, 16. Nov. 1992.

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C.H. Bennett and S.J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states", Phys. Rev. Lett., Vol. 69, No. 20, 1992, pp. 2881--2884.

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C.H. Bennett and S.J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states", Phys. Rev. Lett., Vol. 69, No. 20, 1992, pp. 2881--2884.

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C. H. Bennett and S. Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., 69:2881-- 2884, 1992.

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C.H. Bennett and S.J. Wiesner, "Communication via one- and two-particle operators on einstein- podolskyrosen states," Physical review letters, vol. 69, pp. 2881--2884, 1992.

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Charles H. Bennett and Stephen J. Wiesner. Communication via one- and two-particle operators on einstein-podolsky-rosen states. Phys. Rev. Lett., 69(20):2881-2884, 1993.

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C.H. Bennett, S.J. Wiesner, Communication via One- and Two-Particle Operators on Einstein-Podolsky-Rosen states, Phys. Review Letters, vol.69, 1992, pp. 2881-2884.

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C. H. Bennett and S. J. Wiesner. "Communication via oneand two-particle operators on Einstein-Podolsky-Rosen states." Physical Rev. Letters, pages 2881--2884, 1992.

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C.H. Bennett and S.J. Wiesner, "Communication via one- and two-particle operators on einstein- podolskyrosen states," Physical review letters, vol. 69, pp. 2881--2884, 1992.

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C.H. Bennett, S.J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states", Phys.Rev.Lett. 69(1992)2881--2884

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C.H. Bennett and S.J. Wiesner: "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states", Phys.Rev.Lett. 69(1992) 2881--2884

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C.H. Bennett, S.J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states", Phys.Rev.Lett. 69(1992)2881--2884

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