Optimal local implementation of nonlocal quantum gates

We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [1]. We show: (i) how to implement (weakly) non-local two qubit unitary operations with a small amount of entanglement; (ii) that a known, noisy, non-local unitary operation as well as an unknown, noisy, local unitary operation can be purified; (iii) how to perform the tomography of arbitrary, unknown, non-local operations; (iv) that a set of local unitary operations as well as a set of non-local unitary operations can be stored and compressed; (v) how to implement probabilistically two-qubit gates for photons. We also show how to compress a set of bipartite entangled states locally, as well as how to implement certain non-local measurements using a small amount of entanglement. Finally, we generalize some of our results to multiparty systems. 03.65.Bz, 03.65.Ca, 03.67.Hk

Section: B Purification Of An Unknown Local Noisy Unitary Operationmentioning

confidence: 99%

Section: A Purification Of a Known Non-local Noisy Unitary Operationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlocal operations: Purification, storage, compression, tomography, and probabilistic implementation

Dür

Cirac

2001

“…In particular, the latter effect implies that one can realize the above tasks, such as quantum teleportation [2] starting from one entangling operation. Besides the nonlocal Hamiltonians directly results in the dynamical evolution of distributed quantum systems, thus it is also significative to explore other properties such as the structure and interconvertability of nonlocal gates.In fact, many results have been reported in this direction [3,4,5,6,7,8,9,10,11,12,13,14,15]. Here, a prime problem is the efficiency for implementing a given nonlocal gate.…”

mentioning

confidence: 99%

Probabilistic implementation of a nonlocal operation using a nonmaximally entangled state

Chen

2005

We develop the probabilistic implementation of a nonlocal gate exp [iξσn A σn B ] and ξ ∈ [0, π 4 ], by using a single non-maximally entangled state. We prove that, nonlocal gates can be implemented with a fidelity greater than 79.3% and a consumption of less than 0.969 ebits and 2 classical bits, when ξ ≤ 0.353. This provides a higher bound for the feasible operation compared to the former techniques [9,14,16]. Besides, gates with ξ ≥ 0.353 can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency as the distillation-based protocol [14,16], while our method saves extra classical resource. Gates with ξ → 0 can be implemented with nearly unit probability and a small entanglement. We also generalize some application to the multiple system, where we find it is possible to implement certain nonlocal gates between many non-entangled partners using a non-maximally multiple entangled state.Entanglement has been examined as an essential resource in most applications of quantum information such as enhanced classical communication, dense coding and quantum cryptography [1]. Of all tasks above, the implementation of nonlocal quantum operation on spatially distributed systems is a considerable aspect, especially in quantum computation. This is because, all in all, the only performance by a quantum computer is proved to be the collective unitary operation, which is also able to create entanglement between distributed groups. In particular, the latter effect implies that one can realize the above tasks, such as quantum teleportation [2] starting from one entangling operation. Besides the nonlocal Hamiltonians directly results in the dynamical evolution of distributed quantum systems, thus it is also significative to explore other properties such as the structure and interconvertability of nonlocal gates.In fact, many results have been reported in this direction [3,4,5,6,7,8,9,10,11,12,13,14,15]. Here, a prime problem is the efficiency for implementing a given nonlocal gate. It is accepted that at least the consumption of 1 ebit and 2 cbits is necessarily required to faithfully implement a general nonlocal operation [8]. On the other hand, a remarkable progress has been made by [9], which says gates with small ξ can be implemented by using a lower entanglement and a more classical consumption. However the scheme therein is inefficient for the gates with larger ξ, and it usually requires an excessive amount of classical resource because of plenty of quantum channels required. This deficiency has been made up by the recent work in [14], who employ a probabilistic protocol to implement the nonlocal gates, with a high fidelity when ξ is small. The required classical communication therein is 2 bits, while the entanglement can be made arbitrarily small since it relates to the success fidelity. However, the best attainable fidelity will lower * Electronic address: deteriorate@zju.edu.cn † Electronic address: yxchen@zimp.edu.cn down rapidly with the increasing ξ, thus it is irresponsi...

“…This gate can be performed bi-locally by Alice and Bob if they share one ebit of entanglement per gate use [17]. In our example Alice and Bob share an unknown state from the known list L and try to implement the CNOT gate by LOCC.…”

mentioning

confidence: 99%

Entanglement, discord, and the power of quantum computation

Brodutch

Terno

2011

We show that the ability to create entanglement is necessary for execution of bipartite quantum gates even when they are applied to unentangled states and create no entanglement. Starting with a simple example we demonstrate that to execute such a gate bi-locally the local operations and classical communications (LOCC) should be supplemented by shared entanglement. Our results point to the changes in quantum discord, which is a measure of quantumness of correlations even in the absence of entanglement, as the indicator of failure of a LOCC implementation of the gates.The question "What makes a quantum computer tick?" goes back to the early discussions of quantum algorithms [1]. Two different explanations of the speed-up of quantum algorithms are centered on the two fundamental aspects of quantum theory: superposition of quantum states and their entanglement [2,3].The latter view is supported by the make-up of a universal set of gates [2]. To run a quantum computation it is sufficient to execute certain one-qubit gates and one entangling gate, such as a two-qubit controlled-NOT (CNOT). An entangling gate turns a generic nonentangled input into an entangled output. On the other hand, any pure-state quantum computation that utilizes only a restricted amount of entanglement can be efficiently simulated classically [4].According to the alternative view, it is a superposition of all possible computational paths in a quantum computer that is responsible for a speed-up, while entanglement may be just incidental. Indeed, the algorithm DQC1 demonstrates such a speed-up without entanglement [5,6].We show that entanglement is required for the implementation of bipartite gates, even if they operate on a restricted set L of unentangled input states that are transformed into unentangled outputs. This remains true when the set is chosen to contain only mixtures of some pure states, and not their coherent superpositions.A distributed implementation of a gate is a natural setting to study the effects of entanglement. A(lice) and B(ob) execute a bipartite gate U using local operations and different shared resources. We show that under quite general assumptions U can be implemented bi-locally on L only if Alice and Bob share some entanglement. The build-up of quantum correlations other than entanglement as ρ in is transformed into ρ out indicates the demand for shared entanglement. The correlations are quantified by quantum discord [7].We first introduce quantum discord and review some of its properties, then present a simple example and follow with general results.Discord is defined through the difference in the gen- * Electronic address: aharon.brodutch@mq.edu.au † Electronic address: daniel.terno@mq.edu.au eralizations of two expressions for the classical mutual information,