We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed.
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 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…
Recently Liu, Long, Tong and Li [Phys. Rev. A 65, 022304 (2002)] have proposed a scheme for superdense coding between multiparties. This scheme seems to be highly asymmetric in the sense that only one sender effectively exploits entanglement. We show that this scheme can be modified in order to allow more senders to benefit of the entanglement enhanced information transmission.
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 …
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 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…
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 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 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 describe a method to non-obliviously communicate a 2l-qubit quantum state by physically transmitting l+o(l) qubits of communication, and by consuming l ebits of entanglement and some shared random bits. In the non-oblivious scenario, the sender has a classical description of the state to be communicated. Our method can be used to communicate states that are pure or entangled with the sender's system; l+o(l) and 3l+o(l) shared random bits are sufficient respectively.
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.
We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part of the graph is considered. We show that in this case the dynamics of the quantum walk is independent of the size of the second part and reduces to the one for the star graph where perfect state transfer is achieved. Second, we consider the situation where the sender and the receiver vertex are in the opposite parts of the graph. In such a case the state tr…
We find a protocol transmitting K quantum states crossly in the quantum networks with K pair sender-receiver and one bottleneck channels only with sharing quantum correlations between senders. In these networks senders want to multi cast perfect quantum states to receivers. Perfect send on the quantum networks is impossible just using some additional resources like quantum correlation. This protocol has been used maximum entangled states and Quantum Discord which is best indicator of the quantum nature of the correlation to sharing between senders. At first, to send perfect K states in quantum…
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…
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 …
Perfect state transfer between two marked vertices of a graph by means of discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit calculation that for the coined quantum walks on star graph and complete graph with self-loops perfect state transfer between the sender and receiver vertex is achieved for arbitrary number of vertices $N$ in $O(\sqrt{N})$ steps of the walk. Finally, we show that Szegedy's walk with queries on complete graph allows for state transfer with unit fidelity in the limit o…
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.
In this paper we propose a scheme for quasi-perfect state transfer in a network of dissipative harmonic oscillators. We consider ideal sender and receiver oscillators connected by a chain of nonideal transmitter oscillators coupled by nearest-neighbor resonances. From the algebraic properties of the dynamical quantities describing the evolution of the network state, we derive a criterion, fixing the coupling strengths between all the oscillators, apart from their natural frequencies, enabling perfect state transfer in the particular case of ideal transmitter oscillators. Our criterion provides…
We consider the scenario of deterministic classical information transmission between multiple senders and a single receiver, when they a priori share a multipartite quantum state -- an attempt towards building a deterministic dense coding network. Specifically, we prove that in the case of two or three senders and a single receiver, generalized Greenberger-Horne-Zeilinger (gGHZ) states are not beneficial for sending classical information deterministically beyond the classical limit, except when the shared state is the GHZ state itself. On the other hand, three- and four-qubit generalized W (gW…
In order to understand the resourcefulness of a natural quantum system in quantum communication tasks, we study the dense coding capacity (DCC) and teleportation fidelity (TF) of Haar uniformly generated random multipartite states of various ranks. We prove that when a rank-2 two-qubit state, a Werner state, and a pure state possess the same amount of entanglement, the DCC of a rank-2 state belongs to the envelope made by pure and Werner states. In a similar way, we obtain an upper bound via the generalized Greenberger-Horne-Zeilinger state for rank-2 three-qubit states when the dense coding w…
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.
Quantum superdense coding enables a sender to encode a two-bit classical message in one qubit using the preshared entanglement. In this paper, we develop a superdense coding protocol using a dual quantum Zeno (DQZ) gate to take the full advantage of quantum superdense coding from the complete Bell-state analysis. We verify that the DQZ gate allows remote parties to achieve the distinguishability of orthonormal Bell states in a semi-counterfactual manner and the DQZ superdense coding achieves high throughput efficiency as a function of cycle numbers for the Bell-state analyzer.
We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and quantum side information both at the sender and at the decoder. The available resources are shared entanglement, and noiseless classical and quantum communication channels. We derive one-shot direct and converse bounds for these three resources, represented in terms of the smooth conditional entropies of the source state. Various coding theorems for two-party so…
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.
Suppose that $m$ senders want to transmit classical information to $n$ receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each $m$ and $n$ with $m\ge 2$ or $n\ge 2$, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and i…
We discuss a scheme for a full superdense coding of entangled photon states employing only linear-optics elements. By using the mixed basis consisting of four states that are unambiguously distinguishable by a standard and polarizing beam splitters we can deterministically transfer four messages by manipulating just one of the two entangled photons. The sender achieves the determinism of the transfer either by giving up the control over 50% of sent messages (although known to her) or by discarding 33% of incoming photons.
True tripartite entanglement of the state of a system of three qubits can be classified on the basis of stochastic local operations and classical communications (SLOCC). Such states can be classified in two categories: GHZ states and W-states. It is known that GHZ states can be used for teleportation and superdense coding, but the prototype W-state cannot be. However, we show that there is a class of W-states that can be used for perfect teleportation and superdense coding.
We develop a family of perfect quantum error correcting codes that correct for phase errors that arise on any qubit, at any time, during a perfect state transfer experiment. These ensure that we find the optimal operating regime for corrected state transfer. For a specific class of system, we further show that while dephasing noise can be corrected, depolarising noise cannot.
We investigate the security of generalized quantum multiple-access channels. We provide the formula for the achievable rate region of secure communication in the scenario of two senders and a single receiver. We explicitly specify a protocol for secure communication in this scenario, which employs superdense coding. The protocol is based on the distribution of a tripartite GHZ state. It allows for both symmetric and asymmetric key distribution whereby one of the senders can have twice the capacity of the other sender. We prove the security of the protocol against general quantum attacks, analy…
We present a procedure inspired by dense coding, which enables a highly efficient transmission of information of a continuous nature. The procedure requires the sender and the recipient to share a maximally entangled state. We deal with the concrete problem of aligning reference frames or trihedra by means of a quantum system. We find the optimal covariant measurement and compute the corresponding average error, which has a remarkably simple close form. The connection of this procedure with that of estimating unitary transformations on qubits is briefly discussed.
Previously it was shown that (almost) perfect state transfer can be achieved on the complete bipartite graph by a discrete-time coined quantum walk based algorithm when both the sender and receiver vertices are in the same partition of the graph and when the sender and receiver are in opposite partitions of the same size. By changing the coin operator, we analyze the state transfer problem and we show that it is still possible to achieve state transfer with high fidelity even when the sender and receiver are in different partitions with different sizes. Moreover, it is also possible to use an …
We explicate an example of the so called Task oriented Maximally Entangled states (TMES) in the context of teleportation and superdense coding. In physical situation, this state can emerge from decoherence of more entangled state or may be prepared for the purpose at hand, with less entanglement resource. We find that a variant of the Brown state can be utilized for perfect teleportation of single and two qubit states. In case of superdense coding, it is observed that five cbits can be transmitted by sending only three qubits.
In a network, a channel introduces correlations to the parties that aim to establish a communication protocol. In this work, we present a framework of non-local network coding by exploiting a Bell scenario and show the usefulness of non-local and quantum resources in network coding. Two-sender and two-receiver interference channels are considered, for which network coding is characterized by two-input and four-outcome Bell scenarios. It is shown that non-signaling (quantum) correlations lead to strictly higher channel capacities in general than quantum (local) correlations. It is also shown th…
We investigate how relativistic acceleration of the observers can affect the performance of the quantum teleportation and dense coding for continuous variable states of localized wavepackets. Such protocols are typically optimized for symmetric resources prepared in an inertial frame of reference. A mismatch of the sender's and the receiver's accelerations can introduce asymmetry to the shared entanglement, which has an effect on the efficiency of the protocol that goes beyond entanglement degradation due to acceleration. We show how these asymmetry losses can be reduced by an extra LOCC step …
Recently Xia and Song [Phys. Lett. A (In press)] have proposed a controlled quantum secure direct communication (CQSDC) protocol. They claimed that in their protocol only with the help of the controller Charlie, the receiver Alice can successfully extract the secret message from the sender Bob. In this letter, first we will show that within their protocol the controller Charlie's role can be excluded due to their unreasonable design. We then revise the Xia-Song CQSDC protocol such that its original advantages are retained and the CQSDC can be really realized.
We investigate the usefulness of a recently introduced five qubit state by Brown $\it et al. \normalfont$ \cite{Brown} for quantum teleportation, quantum state sharing and superdense coding. It is shown that this five-qubit state can be utilized for perfect teleportation of arbitrary single and two qubit systems. We devise various schemes for quantum state sharing of an arbitrary single and two particle state via cooperative teleportation. We later show that this state can be used for superdense coding as well. It is found that five classical bits can be sent by sending only three quantum bits…
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…
We conjecture that criterion for perfect quantum teleportation is that the Groverian entanglement of the entanglement resource is $1/\sqrt{2}$. In order to examine the validity of our conjecture we analyze the quantum teleportation and superdense coding with $|Φ> = (1/\sqrt{2}) (|00q_1> + |11q_2>)$, where $|q_1>$ and $|q_2>$ are arbitrary normalized single qubit states. It is shown explicitly that $|Φ>$ allows perfect two-party quantum teleportation and superdense coding scenario. Next we compute the Groverian measures for $|ψ>=\sqrt{1/2 - b^2}|100>+b |010>+a|001> +\sqrt{1/2-a^2}|111>$ and $|\…
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…
An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. A further circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary 1-qubit errors. In addition, the performance of two error correction schemes, one based on the quantum…
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…
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 establish a universal complementarity relation between the capacity of classical information transmission by employing a multiparty quantum state as a multiport quantum channel, and the genuine multipartite entanglement of the quantum state. The classical information transfer is from a sender to several receivers by using the quantum dense coding protocol with the multiparty quantum state shared between the sender and the receivers. The relation holds for arbitrary pure or mixed quantum states of an arbitrary number of parties in arbitrary dimensions.
We consider the compound memoryless quantum multiple-access channel (QMAC) with two sending terminals. In this model, the transmission is governed by the memoryless extensions of a completely positive and trace preserving map which can be any element of a prescribed set of possible maps. We study a communication scenario, where one of the senders aims for transmission of classical messages while the other sender sends quantum information. Combining powerful universal random coding results for classical and quantum information transmission over point-to-point channels, we establish universal co…
We analyze a generalization of Huffman coding to the quantum case. In particular, we notice various difficulties in using instantaneous codes for quantum communication. Nevertheless, for the storage of quantum information, we have succeeded in constructing a Huffman-coding inspired quantum scheme. The number of computational steps in the encoding and decoding processes of N quantum signals can be made to be of polylogarithmic depth by a massively parallel implementation of a quantum gate array. This is to be compared with the O (N^3) computational steps required in the sequential implementatio…
We propose to use ferromagnetic systems for entanglement generation and distribution together with perfect state transfer between distant parties in a qubit chain. The scheme relies on an effective 2-qubit dynamics, realized by leaving two empty sites in a uniformly filled chain. This allows long-range interacting qubit chains to serve as quantum channels for both tasks with optimal performances. Remarkably, the entanglement between sender and receiver sites is independent of both the transmission distance and of system size. This property opens new perspectives for short and mid-range quantum…
This paper considers the communication over a quantum multiple-unicast network where r sender-receiver pairs communicate independent quantum states. We concretely construct a quantum network code for the quantum multiple-unicast network as a generalization of the code [Song and Hayashi, arxiv:1801.03306, 2018] for the quantum unicast network. When the given node operations are restricted to invertible linear operations between bit basis states and the rates of transmissions and interferences are restricted, our code certainly transmits a quantum state for each sender-receiver pair by n-use of …
In the direct communication quantum channels the authorized recipient (Bob) and the non-authorized recipient (Eve) have different abilities for verification of received information. Bob can apply the feedback to commit the sender (Alice) to perform verification. Eve has to use for verification an indirect method based on the measurement of a set of incompatible observables enough for determination of the coding basis used by Alice. In the protocol of direct communication regular modification of coding basis and masking it with an equilibrium in average information carrier density matrix preven…
