Chang-Bao Fu, Shou Zhang, Ke Li, Kyu-Hwang Yeon, Chung-In Um
A two-receiver quantum dense coding scheme and an $N$-receiver quantum dense coding scheme, in the case of non-symmetric Hilbert spaces of the particles of the quantum channel, are investigated in this paper. A sender can send his messages to many receivers simultaneously. The scheme can be applied to quantum secret sharing and controlled quantum dense coding.
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Conditional pulse nulling (CPN) receiver is proposed by Dolinar to discriminate pulse position modulation (PPM) signals. The receiver using a beam splitter and an on-off photon detector can outperform the standard quantum limit (SQL) for PPM signals. In this paper, we apply this receiver to multi-pulse PPM (MPPM) and binary quantum coding signals, and use dynamic programming algorithm to optimize the control strategy. The MPPM signals is used to improve the band-utilization efficiency, and the binary quantum coding make the communication able to correct the error. Numerical simulation results …
We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state…
We present a dense coding scheme between one sender and two receivers, which guarantees that the receivers simultaneously obtain their respective messages. In our scheme, the quantum entanglement channel is first locked by the sender so that the receivers cannot learn their messages unless they collaborate to perform the unlocking operation. We also show that the quantum Fourier transform can act as the locking operator both in simultaneous dense coding and teleportation.
We investigate probabilistic dense coding in non-symmetric Hilbert spaces of the sender's and the receiver's particles. The sender and the receiver share the multipartite non-maximally quantum channel. We also discuss the average information.
We investigate the usefulness of different classes of genuine quadripartite entangled states as quantum resources for teleportation and superdense coding. We examine the possibility of teleporting unknown one, two and three qubit states. We show that one can use the teleportation protocol to send any general one and two qubit states. A restricted class of three qubit states can also be faithfully teleported. We also explore superdense coding protocol in single-receiver and multi-receiver scenarios. We show that there exist genuine quadripartite entangled states that can be used to transmit fou…
We introduce the notion of distributed quantum dense coding, i.e. the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a non-trivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for …
We consider generalisations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide example…
We examine dense coding with an arbitrary pure entangled state sharing between the sender and the receiver. Upper bounds on the average success probability in approximate dense coding and on the probability of conclusive results in unambiguous dense coding are derived. We also construct the optimal protocol which saturates the upper bound in each case.
Distributed Quantum Dense Coding Enhanced With Non-classical Routing
提出分布式量子密集编码协议，通过控制系统叠加编码过程，实现单量子比特系统的非经典路由。在弱纠缠和噪声态下，该协议在解码策略中表现更优，扩展到含噪声信道及多接收方时也有良好性能。
We study optimal dense coding with thermal entangled states of a two-qubit anisotropic \emph{XXZ} model and a Heisenberg model with Dzyaloshinski-Moriya (DM) interactions. The DM interaction is another kind of anisotropic antisymmetric exchange interaction. The effects of these two kinds of anisotropies on dense coding are studied in detail for both the antiferromagnetic and ferromagnetic cases. For the two models, we give the conditions that the parameters of the models have to satisfy for a valid dense coding. We also found that even though there is entanglement, it is unavailable for our op…
The sending station being the classical device can be eavesdropped by classical means. Dense coding and quantum nature of wave function give the additional resource to raise the safety of the quantum channel as a whole.
We study the super dense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and non-unitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The super dense coding capacity for some special channels and resource states is derived for unitary encoding. We also provide an example of a memory channel where non-unitary encoding leads to an improvement in the super dense coding capacity.
We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed form expression of the dense coding capacity for the cases of two and three senders that involve sharing …
We present a scheme of probabilistic dense coding via a quantum channel of non-maximally entangled three-particle state. The quantum dense coding will be succeeded with a certain probability if the sender introduces an auxiliary particle and performs a collective unitary transformation. Furthermore, the average information transmitted in this scheme is calculated.
The effects of nuclear field and spin-orbit interaction on dense coding and swap operation are studied in detail for both the antiferromagnetic (AFM) and ferromagnetic (FM) coupling cases. The conditions for a valid dense coding and under which swap operation is feasible are given.
A protocol of quantum dense coding protection of two qubits is proposed in amplitude damping (AD) channel using weak measurement and reversal measurement. It is found that the capacity of quantum dense coding under the weak measurement and reversal measurement is always greater than that without weak measurement and reversal measurement. When the protocol is applied, for the AD channels with different damping coefficient, the result reflects that quantum entanglement can be protected and quantum dense coding becomes successful.
We present a rigorous proof of an interesting boundary effect of deterministic dense coding first observed by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Namely, it is shown that $d^2-1$ cannot be the maximal alphabet size of any isometric deterministic dense coding schemes utilizing $d$-level partial entanglement.
Capacity of dense coding via correlated noisy channel is greater than that in uncorrelated noisy channel. It is shown that weak measurement and reversal measurement can make further effort to improve quantum dense coding capacity in correlated amplitude damping channel, but this effort is very small in correlated phase damping channel and correlated depolarizing channel.
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dense coding in terms of the various measures of entanglement and in terms of the average mutual distinguishability of the signal states.
Dense coding or super-dense coding in the case of high-dimension quantum states between two parties and multi-parties has been studied in this paper. We construct explicitly the measurement basis and the forms of the single-body unitary operations corresponding to the basis chosen, and the rules for selecting the one-body unitary operations in a multi-party case.
A scheme to achieve dense quantum coding for the quadrature amplitudes of the electromagnetic field is presented. The protocol utilizes shared entanglement provided by nondegenerate parametric down conversion in the limit of large gain to attain high efficiency. For a constraint in the mean number of photons n associated with modulation in the signal channel, the channel capacity for dense coding is found to be ln(1+n+n^2), which always beats coherent-state communication and surpasses squeezed-state communication for n>1. For n>>1, the dense coding capacity approaches twice that of either sche…
The quantum advantage of dense coding is studied, considering general encoding quantum operations. Particular attention is devoted to the case of many senders, and it is shown that restrictions on the possible operations on the senders' side may make some quantum state useless for dense-coding. It is shown, e.g., that some states are useful for dense coding if the senders can communicate classically (but not quantumly), yet they cannot be used for dense coding, if classical communication is not allowed. These no-go results are actually independent of the particular quantification of the quantu…
We investigate a scheme for implementing quantum dense coding via atomic ensembles, where prior distribution of the quantum entangled state is not needed. Our scheme also combines another two distinct advantages: atomic ensembles qubits with long coherent time serve as memory qubits and phtonic qubit as flying qubit. Thus our suggestion may offer a simple and easy way of demonstrating quantum dense coding experimentally via atomic ensembles.
We introduce a probabilistic version of the one-shot quantum dense coding protocol in both two- and multiport scenarios, and refer to it as conclusive quantum dense coding. Specifically, we analyze the corresponding capacities of two-qubit, two-qutrit, and three-qubit shared states. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities, and the bipartite and multipartite entanglements of the shared state.
We investigate super dense coding in the presence of noise, i.e. the subsystems of the entangled resource state have to pass a noisy unital quantum channel between the sender and the receiver. We discuss explicitly the case of Pauli channels in arbitrary dimension and derive the super dense coding capacity (i.e. the optimal information transfer) for some given resource states. We also study the case that the initial resource state can be chosen: for the qubit depolarizing channel we show that there is a threshold value for the noise parameter, below which the super dense coding protocol is opt…
We investigate the conditions under which unconditional dense coding can be achieved using continuous variable entanglement. We consider the effect of entanglement impurity and detector efficiency and discuss experimental verification. We conclude that the requirements for a strong demonstration are not as stringent as previously thought and are within the reach of present technology.
Capacity Enhancement of n-GHZ State Super-dense Coding Channels by Purification and Quantum Neural Network
提出基于n-GHZ态的超密编码协议，结合纠缠纯化与量子神经网络提升信道容量，实验验证二者叠加增强效果显著。
We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing symmetric normalized Hadamard matrices. In addition, some explicit and conceivable forms for the unitary operators are presented by using some introduced basic operators. It is shown that, the proposed version is logarithmically efficient than some other multi-qubit dense coding protocols.
We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a receiver want to perfectly communicate messages through a one-way classical noisy channel. If the two parties are allowed to share entanglement, there are several positive results that show the existence of channels for which they can communicate strictly more than what they could do with classical resources. In the first task, one sender wants to communicat…
I investigate dense coding with a general mixed state on the Hilbert space $C^{d}\otimes C^{d}$ shared between a sender and receiver. The following result is proved. When the sender prepares the signal states by mutually orthogonal unitary transformations with equal {\it a priori} probabilities, the capacity of dense coding is maximized. It is also proved that the optimal capacity of dense coding $χ^{*}$ satisfies $E_{R}(ρ)\leq χ^{*}\leq E_{R}(ρ)+\log_{2}d$, where $E_{R}(ρ)$ is the relative entropy of entanglement of the shared entangled state.
An asymptotic entanglement measure for any bipartite states is derived in the light of the dense coding capacity optimized with respect to local quantum operations and classical communications. General properties and some examples with explicit forms of this entanglement measure are investigated.
Usually it is assumed that quantum dense coding is due to quantum entanglement between two parties. We show that this phenomenon has its origin in {\em correlations} between two parties rather than simply in entanglement. In order to justify our argument we evaluate a capacity of the noiseless channel for two cases: (1) when Bob performs measurement just on the particle received from Alice and (2) in the case when he utilizes the whole potential of the dense coding, that is, he performs the measurement on the received particle and the particle he had prior to the communication. We also present…
We investigate a secure scheme for implementing quantum dense coding via cavity decay and liner optics devices. Our scheme combines two distinct advantages: atomic qubit sevres as stationary bit and photonic qubit as flying bit, thus it is suitable for long distant quantum communication.
Dense coding has been implemented using the generalized Grover's algorithm and its inverse operation. Exploiting the superpositions of two Einstein-Podolsky-Rosen (EPR) states, messages that are possible to be transmitted increase. Our scheme is demonstrated using nuclear magnetic resonance (NMR). Experimental results show a good agreement between theory and experiment.
An (n,1,p)-Quantum Random Access (QRA) coding, introduced by Ambainis, Nayak, Ta-shma and Vazirani in ACM Symp. on Theory of Computing 1999, is the following communication system: The sender which has n-bit information encodes his/her information into one qubit, which is sent to the receiver. The receiver can recover any one bit of the original n bits correctly with probability at least p, through a certain decoding process based on positive operator-valued measures. Actually, Ambainis et al. shows the existence of a (2,1,0.85)-QRA coding and also proves the impossibility of its classical coun…
In a recent Brief Report, Lee et al. [L. Lee, D. Ahn, and S.W. Hwang, Phys. Rev. A 66, 024304 (2002)] have claimed that using pairwise entangled qubits gives rise to an exponentially more efficient dense coding when two parties are involved than using maximally entangled qubits shared among N parties. Here, we show that their claim is not true.
Simultaneous dense coding guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to "lock" the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on simultaneous dense coding: (1) We propose three simultaneous dense coding protocols, which use different $N$-dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the…
We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be ``tight'' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d^2 signals. A general construction procedure for orthono…
We study multipartite super dense coding in the presence of a covariant noisy channel. We investigate the case of many senders and one receiver, considering both unitary and non-unitary encoding. We study the scenarios where the senders apply local encoding or global encoding. We show that, up to some pre-processing on the original state, the senders cannot do better encoding than local, unitary encoding. We then introduce general Pauli channels as a significant example of covariant maps. Considering Pauli channels, we provide examples for which the super dense coding capacity is explicitly de…
The paper presents the detailed study of controlled dense coding scheme for different types of $3$ and $4-$ particle states. It consists of GHZ state, GHZ type states, Maximal Slice state, Four particle GHZ state and W class of states. It is shown that GHZ-type states can be used for controlled dense coding in a probabilistic sense. We have shown relations among parameter of GHZ type state, concurrence of the shared bipartite state by two parties with respect to GHZ type and Charlie's measurement angle $θ$. We have seen that tripartite W state and quadripartite W state cannot be used in contro…
A set of protocols for teleportation and dense coding tasks with the use of a N particle quantum channel, presented by entangled states of the GHZ class, is introduced, when N>2. Using a found representation for the multiparticle entangled states of the GHZ class, it has shown, that for dense coding schemes enhancement of the classical capacity of the channel due from entanglement is N/N-1. If N>2 there is no one - to -one correspondence between teleportation and dense coding schemes in comparison with the EPR channel is exploited. A set of schemes, for which two additional operations as entan…
We proposed a scheme of continuous-variable quantum key distribution, in which the bright Einstein-Podolsky-Rosen entangled optical beams are utilized. The source of the entangled beams is placed inside the receiving station, where half of the entangled beams are transmitted with round trip and the other half are retained by the receiver. The amplitude and phase signals modulated on the signal beam by the sender are simultaneously extracted by the authorized receiver with the scheme of the dense-coding correlation measurement for continuous quantum variables, thus the channel capacity is signi…
The remarkable transmission of two bits of information via a single qubit entangled with another at the destination, is presented as an expansion of the unremarkable classical circuit that transmits the bits with two direct qubit-qubit couplings between source and destination
In this paper we propose a technique for distributing entanglement in architectures in which interactions between pairs of qubits are constrained to a fixed network $G$. This allows for two-qubit operations to be performed between qubits which are remote from each other in $G$, through gate teleportation. We demonstrate how adapting \emph{quantum linear network coding} to this problem of entanglement distribution in a network of qubits can be used to solve the problem of distributing Bell states and GHZ states in parallel, when bottlenecks in $G$ would otherwise force such entangled states to …
In this paper, we show how continuous-variable dense coding can be implemented using entangled light generated from a membrane-in-the-middle geometry. The mechanical resonator is assumed to be a high reflectivity membrane hung inside a high quality factor cavity. We show that the mechanical resonator is able to generate an amount of entanglement between the optical modes at the output of the cavity, which is strong enough to approach the capacity of quantum dense coding at small photon numbers. The suboptimal rate reachable by our optomechanical protocol is high enough to outperform the classi…
The utilization of a $d$-level partially entangled state, shared by two parties wishing to communicate classical information without errors over a noiseless quantum channel, is discussed. We analytically construct deterministic dense coding schemes for certain classes of non-maximally entangled states, and numerically obtain schemes in the general case. We study the dependency of the information capacity of such schemes on the partially entangled state shared by the two parties. Surprisingly, for $d>2$ it is possible to have deterministic dense coding with less than one ebit. In this case the …
We investigate the dense coding in the case of non-symmetric Hilbert spaces of the sender and receiver's particles sharing the quantum maximally entangled state. The efficiency of classical information gain is also considered. We conclude that when a more level particle is with the sender, she can get a non-symmetric quantum channel from a symmetric one by entanglement transfer. Thus the efficiency of information transmission is improved.
We consider the possibility of using stabilizer states to perform deterministic dense coding among multiple senders and a single receiver. In the model we studied, the utilized stabilizer state is partitioned into several subsystems and then each subsystem is held by a distinct party. We present a sufficient condition for a stabilizer state to be useful for deterministic distributed dense coding with respect to a given partition plan. The corresponding protocol is also constructed. Furthermore, we propose a method to partially solve a more general problem of finding the set of achievable alpha…
A complementarity relation is established between the capacity of multiport classical information transmission via quantum states and multiparty quantum correlation measures for three-qubit pure states. The multiparty quantum correlation measures considered are the generalized geometric measure, the tangle, and the discord monogamy score. The complementarity relation is revealed by the identification of a one-parameter family of pure three-qubit states, which we call the maximally dense coding capable family of states. These states have the maximal multiport dense coding capacity among all thr…
A controlled quantum dense coding scheme is investigated with a four-particle non-maximal quantum channel. The amount of classical information is shown to be capable of being controlled by the controllers through adjustments of the local measurement angles and to depend on the coefficients of the quantum channel; in addition, the four particles are distributed in two inverse ways in such an quantum channel. A restricted condition for distributing the particles to realize quantum dense coding in an arbitrary ($N+2$)-particle quantum channel is proposed.
The quantum cost is a key ingredient to evaluate the quality of quantum protocols from a practical viewpoint. We show that the quantum cost of d-dimensional dense coding protocol is equal to d+3 when transmitting the classical message (0,0), and that is equal to d+4 when transmitting other classical message. It appears linear growth with the dimension and thus makes sense for implementation. In contrast, the quantum cost of high-dimensional teleportation protocols is equal to 13, which is the maximum value of the cost for the two-dimensional case. As an application, we establish the relation b…
We propose quantum dense coding protocol for optical images. This protocol extends the earlier proposed dense coding scheme for continuous variables [S.L.Braunstein and H.J.Kimble, Phys.Rev.A 61, 042302 (2000)] to an essentially multimode in space and time optical quantum communication channel. This new scheme allows, in particular, for parallel dense coding of non-stationary optical images. Similar to some other quantum dense coding protocols, our scheme exploits the possibility of sending a classical message through only one of the two entangled spatially-multimode beams, using the other one…
The question of the measurements on the Bell states by making use of mode change (from mixed to pure) of one qubit is considered. Such a mode change cannot be taken advantage of for superluminal communication in teleportation, and it may define constraints on the size of the gates.
In this paper, we study quantum dense coding between two arbitrarily fixed particles in a (N+2)-particle maximally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted classical information amount through such an entangled quantum channel usually is less than two classical bits. However, the information amount may reach two classical bits of information, and the classical information capacity is independent of the number of the entangled particles in the initial entangled state under certain conditions. The results offer …
In this paper, we provide an operational criterion for controlled dense coding with a general class of three-qubit partially entangled states. A general three-qubit pure entangled state can be classified into two inequivalent classes according to their genuine tripartite entanglement. We claim that if a three-qubit state shows entanglement characteristic similar to $GHZ$-class then such non-trivial tripartite states are useful in {\it controlled dense coding} whereas states belonging to $W$-class are not useful for that. We start with a particular class of non-trivial partially entangled state…
We study the performance of the super dense coding protocol in the presence of quantum channels with covariant noise. We first consider the bipartite case and review in a unified way the case of general Pauli channels. We discuss both the cases of unitary and non-unitary encoding. We also study the multipartite scenario and investigate the case of many senders and one receiver.
A tripartite entangled state of bright optical field is experimentally produced using an Einstein-Podolsky-Rosen entangled state for continuous variables and linear optics. The controlled dense coding among a sender, a receiver and a controller is demonstrated by exploiting the tripartite entanglement. The obtained three-mode position correlation and relative momentum correlation between the sender and the receiver and thus the improvements of the measured signal to noise ratios of amplitude and phase signals with respect to the shot noise limit are 3.28dB and 3.18dB respectively. If the mean …
A quantum steganography protocol with large payload is proposed, based on dense coding and entanglement swapping of GHZ states. Its super quantum channel is formed by building up the hidden channel within the original quantum secure direct communication (QSDC) scheme. Based on the original QSDC, secrets messages are transmitted by integrating dense coding of GHZ states and entanglement swapping of GHZ states. Its capacity of super quantum channel achieves six bits per round covert communication, much higher than the previous quantum steganography protocols. Its imperceptibility is good, since …
Quantum dense coding is a protocol for transmitting two classical bits of information from a sender (Alice) to a remote receiver (Bob) by sending only one quantum bit (qubit). In this article, we propose an experimentally feasible scheme to realize quantum dense coding \textit{via} entanglement swapping in a cavity array containing a certain number of two-level atoms. Proper choice of system parameters such as atom-cavity couplings and inter-cavity couplings allows perfect transfer of information. A high fidelity transfer of information is shown to be possible by using recently achieved experi…
Quantum dense coding is one of the most important protocols in quantum communication. It derives from the idea of using quantum resources to boost the communication capacity and now serves as a key primitive across a variety of quantum information protocols. Here, we focus on the basic theoretical ideas behind quantum dense coding, discussing its development history from discrete and continuous variables to quantum networks, then to its variant protocols and applications in quantum secure communication. With this basic background in hand, we then review the main experimental achievements, from…
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