We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in 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 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 results in less communication than is required with only classical 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 remote parties.
We present a simple communication complexity problem where three parties benefit from sharing bound entanglement. This demonstrates that entanglement distillability of the shared state is not necessary in order to surpass classical communication complexity.
We consider composability of quantum channels from a limited amount of entanglement via local operations and classical communication (LOCC). We show that any $k$-partially entanglement breaking channel can be composed from an entangled state with Schmidt number of $k$ via one-way LOCC. From the entanglement assisted construction we can reach an alternative definition of partially entanglement breaking channels.
Bipartite operations underpin both classical communication and entanglement generation. Using a superposition of classical messages, we show that the capacity of a two-qubit operation for error-free entanglement-assisted bidirectional classical communication can not exceed twice the entanglement capability. In addition we show that any bipartite two-qubit operation can increase the communication that may be performed using an ensemble by twice the entanglement capability.
Phenomena induced by the existence of entanglement, such as nonlocal correlations, exhibit characteristic properties of quantum mechanics distinguishing from classical theories. When entanglement is accompanied by classical communication, it enhances the power of quantum operations jointly performed by two spatially separated parties. Such a power has been analyzed by the gap between the performances of joint quantum operations implementable by local operations at each party connected by classical communication with and without the assistance of entanglement. In this work, we present a new for…
Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an en…
We show that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data is distributed among remote parties. 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 one of them to learn the value of the function with only two bits of communication occurring among the parties, whereas, without quantum entanglement, three bits of communication are necessary. This result contrasts the well-known fact that quantum entanglemen…
We present an improved protocol for entanglement purification of bipartite mixed states. The protocol requires two-way classical communication and hence implies an improved lower bound on the quantum capacity with two-way classical communication of the quantum depolarizing channel.
Entanglement is at the heart of fundamental tests of quantum mechanics like tests of Bell-inequalities and, as discovered lately, of quantum computation and communication. Their technological advance made entangled photons play an outstanding role in entanglement physics. We give a generalized concept of qubit entanglement and review the state of the art of photonic experiments.
Entanglement is an essential resource in current experimental implementations for quantum information processing. We review a class of experiments exploiting photonic entanglement, ranging from one-way quantum computing over quantum communication complexity to long-distance quantum communication. We then propose a set of feasible experiments that will underline the advantages of photonic entanglement for quantum information processing.
Entanglement bits or ``ebits'' have been proposed as a quantitative measure of a fundamental resource in quantum information processing. For such an interpretation to be valid, it is important to show that the same number of ebits in different forms or concentrations are inter-convertible in the asymptotic limit. Here we draw attention to a very important but hitherto unnoticed aspect of entanglement manipulation --- the classical communication cost. We construct an explicit procedure which demonstrates that for bi-partite pure states, in the asymptotic limit, entanglement can be concentrated …
We consider the problem of remote state preparation recently studied in several papers. We study the communication complexity of this problem, in the presence of entanglement and in the scenario of single use of the channel.
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed inputs can be turned into a quantum communication protocol. As an application of this bound, we give a very simple proof of the statement that almost all Boolean functions on n+n bits have linear communication complexity, even in the presence of unlimited entanglement.
We present an one-time-pad key communication protocol that allows secure direct communication with entanglement. Alice can send message to Bob in a deterministic manner by using local measurements and public communication. The theoretical efficiency of this protocol is double compared with BB84 protocol. We show this protocol is unconditional secure under arbitrary quantum attack. And we discuss that this protocol can be perfectly implemented with current technologies.
We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement swapping operations and solve numerically for up to three intermediate entanglement swapping operations. Our model yields two-photon interference visibilities post-selected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication dist…
We pose the fundamental question of communication properties of primitives irrespectively of their implementation. To illustrate the idea we introduce the concept of entanglement-swapping boxes, i.e. we consider any quantum operations which perform entanglement swapping, not necessarily via simple quantum teleportation. We ask a question about the properties of such boxes., i.e. what local operations and how much classical communication are needed to perform them. We also ask if any box which performs entanglement swapping can be used to establish classical communication. We show that each box…
In a recent paper [Phys. Rev. A 76, 032304(2007)], Li et al. proposed the definition of the residual entanglement for n qubits by means of the Stochastic local operations and classical communication. Here we argue that their definition is not suitable for the case of odd-n qubits.
Communication rates over quantum channels can be boosted by entanglement, via superadditivity phenomena or entanglement assistance. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses. Nevertheless, when unlimited entanglement assistance is available, the entanglement between channel uses becomes unnecessary -- the entanglement-assisted (EA) capacity of a single-sender and single-receiver channel is additive. We generalize the additivity of EA capacity to general multiple-access channels (MACs) for the total communication rate. Furthermore, fo…
L. Lamata et al. have presented an entanglement classification of four qubits under stochastic local operation and classical communication (SLOCC) based on inductive approach [Phys. Rev. A \textbf{75}, 022318 (2007)]. While it works well for three qubits, we show that some of the families for four qubits have overlaps and hence this approach is not valid for entanglement classification of four or more qubits under SLOCC.
We show a deterministic secure direct communication protocol using single qubit in mixed state. The security of this protocol is based on the security proof of BB84 protocol. It can be realized with current technologies.
We propose a protocol for deterministic communication that does not make use of entanglement. It exploits nonorthogonal states in a two-way quantum channel attaining significant improvement of security and efficiency over already known cryptographic protocols. The presented scheme, being deterministic, can be devoted to direct communication as well as to key distribution, and its experimental realization is feasible with present day technology.
We recall several cryptographic protocols based on entanglement alone and also on entanglement swapping. We make an exposition in terms of the geometrical aspects of the involved Hilbert spaces, and we concentrate on the formal nature of the used transformations.
Extending the eavesdropping strategy devised by Zhang, Li and Guo [Phys. Rev. A 63, 036301 (2001)], we show that the multiparty quantum communication protocol based on entanglement swapping, which was proposed by Cabello [quant-ph/0009025], is not secure. We modify the protocol so that entanglement swapping can secure multiparty quantum communication, such as multiparty quantum key distribution and quantum secret sharing of classical information, and show that the modified protocol is secure against the Zhang-Li-Guo's strategy for eavesdropping as well as the basic intercept-resend attack.
We present basics of mixed-state entanglement theory. The first part of the article is devoted to mathematical characterizations of entangled states. In second part we discuss the question of using mixed-state entanglement for quantum communication. In particular, a type of entanglement that is not directly useful for quantum communcation (called bound entanglement) is analysed in detail.
We propose a probabilistic two-party communication complexity scenario with a prior nonmaximally entangled state, which results in less communication than that is required with only classical random correlations. A simple all-optical implementation of this protocol is presented and demonstrates our conclusion.
Entanglement is known to boost the efficiency of classical communication. In distributed computation, for instance, exploiting entanglement can reduce the number of communicated bits or increase the probability to obtain a correct answer. Entanglement-assisted classical communication protocols usually consist of two successive rounds: first a Bell test round, in which the parties measure their local shares of the entangled state, and then a communication round, where they exchange classical messages. Here, we go beyond this standard approach and investigate adaptive uses of entanglement: we al…
We establish a framework to study the classical-communication properties of primitive local operations assisted by classical communication which realize various redistributions of entanglement, like, e.g., entanglement swapping. On the one hand, we analyze what local operations and how much classical communication are needed to perform them. On the other hand, we investigate whether and to what extent such primitives can help to establish classical communication when they are used in the form of black boxes available to spatially-separated users. In particular, we find that entanglement swappi…
Entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of sqrt(N) bits. Our main result is to prove this prior art result optimal up to a constant factor; any procedure for creating N partially entangled states from singlets requires Omega(sqrt(N)) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transforms. We also prove a lower bound on the inefficiency of the process: to dilute singlets to …
Entanglement assistance is known to reduce the quantum communication complexity of evaluating functions with distributed inputs. But does the type of entanglement matter, or are EPR pairs always sufficient? This is a natural question because in several other settings maximally entangled states are known to be less useful as a resource than some partially entangled state. These include non-local games, tasks with quantum communication between players and referee, and simulating bipartite unitaries or communication channels. By contrast, we prove that the bounded-error entanglement-assisted quan…
Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of complexity. The complexity of entanglement is at the root of the onset of quantum chaos, universal distribution of entanglement spectrum statistics, hardness of a disentangling algorithm and of the quantum machine learning of an unknown random circuit, and universal temporal entanglement fluctuations. In this paper, we numerically show how a crossover from a simple …
We adopt the view according to which information is the primary physical entity that posseses objective meaning. Basing on two postulates that (i) entanglement is a form of quantum information corresponding to internal energy (ii) sending qubits corresponds to work, we show that in the closed bipartite quantum communication systems the information is conserved. We also discuss entanglement-energy analogy in context of the Gibbs-Hemholtz-like equation connecting the entanglement of formation, distillable entanglement and bound entanglement. Then we show that in the deterministic protocols of di…
The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms of the quantum mutual information and does not increase in the presence of a noiseless quantum feedback channel from receiver to sender. In this work, we investigate second-order asymptotics of the entanglement-assisted classical communication task. That is, we consider how quickly the rates of entanglement-assisted codes converge to the entanglement-assisted…
Entanglement monotone is defined as a convex measure of entanglement that does not increase on average under local operations and classical communication (LOCC). Here we call an entanglement monotone a strict entanglement monotone (SEM) if it decreases strictly on average under LOCC. We show that, for any convex roof extended entanglement monotone that on pure states is given by a function of the reduced states, if the function is strictly concave, then it is a SEM. Moreover, we prove that the negativity and the relative entropy of entanglement, which are not defined by the convex roof structu…
We develop a model for a noisy communication channel in which the noise affecting consecutive transmissions is correlated. This model is motivated by fluctuating birefringence of fiber optic links. We analyze the role of entanglement of the input states in optimizing the classical capacity of such a channel. Assuming a general form of an ensemble for two consecutive transmissions, we derive tight bounds on the classical channel capacity depending on whether the input states used for communication are separable or entangled across different temporal slots. This result demonstrates that by an ap…
Stochastic local operations and classical communication (SLOCC), also called local filtering operations, are a convenient, useful set of quantum operations in grasping essential properties of entanglement. We give a quick overview about the characteristics of multipartite entanglement in terms of SLOCC, illustrating the 2-qubit and the rest (2 x 2 x n) quantum system. This not only includes celebrated results of 3-qubit pure states, but also has implications to 2-qubit mixed states.
The ability to unconditionally verify the location of a communication receiver would lead to a wide range of new security paradigms. However, it is known that unconditional location verification in classical communication systems is impossible. In this work we show how unconditional location verification can be achieved with the use of quantum communication channels. Our verification remains unconditional irrespective of the number of receivers, computational capacity, or any other physical resource held by an adversary. Quantum location verification represents a new application of quantum ent…
Natural particle-number entanglement resides between spatial modes in coherent ultra-cold atomic gases. However, operations on the modes are restricted by a superselection rule that forbids coherent superpositions of different particle numbers. This seemingly prevents mode entanglement being used as a resource for quantum communication. In this paper, we demonstrate that mode entanglement of a single massive particle can be used for dense coding and quantum teleportation despite the superselection rule. In particular, we provide schemes where the dense coding linear photonic channel capacity i…
Entanglement appears under two different forms in quantum theory, namely as a property of states of joint systems and as a property of measurement eigenstates in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We show that even in the more constraining bilocal scenario where distant sources of particles are assumed to be independent, i.e. to share no prior randomness, this process can be simulated classically with bounded communication, using only 9 b…
Entanglement appears in two different ways in quantum mechanics, namely as a property of states and as a property of measurement outcomes in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We investigate the communication cost of classically simulating this process. While the communication cost of simulating nonlocal correlations of entangled states appears to be generally quite low, we show here that infinite communication is required to simulate ent…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.
We present two groups of practical entanglement concentration protocols (ECPs) for optical hybrid entangled state (HES). In the first group, it contains two ECPs and both ECPs do not need to know the initial coefficients of the less-entangled state. The second group contains three ECPs and they need to know the initial coefficients. It is shown that the yield of the entanglement concentration in the second group is greater than the first group. Moreover, some protocols are based on the linear optics and can be easily realized under current experiment condition. These protocols may be useful in…
We present Authenticated Multiuser Quantum Direct Communication(MQDC) protocols using entanglement swapping. Quantum direct communication is believed to be a safe way to send a secret message without quantum key distribution. The authentication process in our protocol allows only proper users to participate in communication. In the communication stage after the authentication, any two authorized users among n users can communicate each other even though there is no quantum communication channels between them. For this protocol, we need only n quantum communication channels between the authenti…
We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR pairs, and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. Whil…
In this paper, a bidirectional quantum teleportation protocol based on Einstein-Podolsky-Rosen (EPR) pairs and entanglement swapping is proposed. In this scheme, two users can simultaneously transmit an unknown single-qubit state to each other. The implementation of the proposed scheme is easier in experiment as compared to previous work. By utilizing this bidirectional quantum teleportation protocol, a bidirectional quantum secure direct communication scheme without carrying secret message is presented. Therefore, in the case of using perfect quantum channel, the protocol is completely secure…
We consider implementations of a bipartite unitary on many pairs of unknown input states by local operation and classical communication assisted by shared entanglement. We investigate to what extent the entanglement cost and the classical communication cost can be compressed by allowing nonzero but vanishing error in the asymptotic limit of infinite pairs. We show that a lower bound on the minimal entanglement cost, the forward classical communication cost, and the backward classical communication cost per pair is given by the Schmidt strength of the unitary. We also prove that an upper bound …
Atomic ensembles are effective memory nodes for quantum communication network due to the long coherence time and the collective enhancement effect for the nonlinear interaction between an ensemble and a photon. Here we investigate the possibility of achieving the entanglement distillation for nonlocal atomic ensembles by the input-output process of a single photon as a result of cavity quantum electrodynamics. We give an optimal entanglement concentration protocol (ECP) for two-atomic-ensemble systems in a partially entangled pure state with known parameters and an efficient ECP for the system…
Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure scenarios in the last decade. Here, we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focusing on entanglement-assisted prepare-and-…
We analyse the role of entanglement for transmission of classical information through a memoryless depolarising channel. Using the isotropic character of this channel we prove analytically that the mutual information cannot be increased by encoding classical bits into entangled states of two qubits.
We present a single-photon entanglement concentration protocol for long-distance quantum communication with quantum nondemolition detector. It is the first concentration protocol for single-photon entangled states and it dose not require the two parties of quantum communication to know the accurate information about the coefficient $α$ and $β$ of the less entangled states. Also, it does not resort to sophisticated single-photon detectors, which makes this protocol more feasible in current experiments. Moreover, it can be iterated to get a higher efficiency and yield. All these advantages maybe…
A novel communication protocol based on an entangled pair of qubits is presented, allowing secure direct communication from one party to another without the need for a shared secret key. Since the information is transferred in a deterministic manner, no qubits have to be discarded and every qubit carries message information. The security of the transfer against active and passive eavesdropping attacks is provided. The detection rate of active attacks is at least 25%. The protocol works with a quantum efficiency of 1 bit per qubit transmitted.
We consider properties of states of many qubits, which arise after sending certain entangled states via various noisy channels (white noise, coloured noise, local depolarization, dephasing and amplitude damping). Entanglement of these states is studied and their ability to violate certain classes of Bell inequalities. States which violate them allow for higher than classical efficiency of solving related distributed computational tasks with constrained communication. This is a direct property of such states -- not requiring their further modification via stochastic local operations and classic…
The distribution of entangled states between distant locations will be essential for the future large scale realization of quantum communication schemes such as quantum cryptography and quantum teleportation. Because of the unavoidable noise in the quantum communication channel, the entanglement between two particles is more and more degraded the further they propagate. Entanglement purification is thus essential to distill highly entangled states from less entangled ones. Existing general purification protocols are based on the quantum controlled-NOT (CNOT) or similar quantum logic operations…
We present an economical setup for faithful entanglement sharing against collective noise. It is composed of polarizing beam splitters, half wave plates, polarization independent wavelength division multiplexers, and frequency shifters. An arbitrary qubit error on the polarization state of each photon in a multi-photon system caused by the noisy channel can be rejected, without resorting to additional qubits, fast polarization modulators, and nondestructive quantum nondemolition detectors. Its success probability is in principle 100%, which is independent of the noise parameters, and it can be…
We present a formal quantum mechanical analysis of the communication protocol of Prevedel {\it et al.}\ [Phys. Rev. Lett. \textbf{106}, 110505 (2011)], in which entanglement shared by sender and receiver is used to enhance, beyond that achievable via the optimal classical strategy, the probability of successful transmission of a bit through a particular noisy classical channel ${\cal N}$. We provide a full analysis of this protocol when the shared entanglement resides in a two-qubit system. Our analysis shows the measurement choices specified by the protocol yield the maximum possible enhancem…
