The famous superdense coding protocol of Bennett and Wiesner demonstrates that it is possible to communicate two bits of classical information by sending only one qubit and using a shared EPR pair. Our first result is that an arbitrary protocol for achieving this task (where there are no assumptions on the sender's encoding operations or the dimension of the shared entangled state) is locally equivalent to the canonical Bennett-Wiesner protocol. In other words, the superdense coding task is rigid. In particular, we show that the sender and receiver only use additional entanglement (beyond the EPR pair) as a source of classical randomness.
We also investigate several questions about higher-dimensional superdense coding, where the goal is to communicate one of $d^2$ possible messages by sending a $d$-dimensional quantum state, for general dimensions $d$. Unlike the $d=2$ case (i.e. sending a single qubit), there can be inequivalent superdense coding protocols for higher $d$. We present concrete constructions of inequivalent protocols, based on constructions of inequivalent orthogonal unitary bases for all $d > 2$. Finally, we analyze the performance of superdense coding protocols where the encoding operators are independently sampled from the Haar measure on the unitary group. Our analysis involves bounding the distinguishability of random maximally entangled states, which may be of independent interest.
We analyze quantum superdense coding as would be seen in Everett's many worlds interpretation of measurement, and compare it to Everettian teleportation.
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.
This paper shows how network coding and superdense coding can be combined to increase the classical data throughput by a factor $2-ε$ (for arbitrarily small $ε> 0$) compared to the maximum that could be achieved using either network coding or superdense coding alone. Additionally, a general decomposition of a ``mixed'' network (i.e., consisting of classical and quantum links) is given, and it is reasoned that, owing to the inherent hardness of finding network codes, this may well lead to an increase in classical data throughput in practise, should a scenario arise in which quantum networks are…
We define an anti-quantum bit state via analogous way as the anti-state in Particle Physics.We show the quantum information Feymann diagrams for the teleportations and superdense coding, which preserve the information flow. The role of information vacuum and anihilation between error information and anti-information is mentioned for the stability of quantum computing.
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 study superdense coding with uniformly accelerated particle in single mode approximation and beyond single mode approximation. We use four different functions, the capacity of superdense coding, negativity, discord and the probability of success for evaluating the final results. In single mode approximation, all the four functions behave as expected, however in beyond single mode approximation, except the probability of success, the other three functions represent peculiar behaviors at least for special ranges where the beyond single mode approximation is strong.
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.
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.
Classical communication through quantum channels may be enhanced by sharing entanglement. Superdense coding allows the encoding, and transmission, of up to two classical bits of information in a single qubit. In this paper, the maximum classical channel capacity for states that are not maximally entangled is derived. Particular schemes are then shown to attain this capacity, firstly for pairs of qubits, and secondly for pairs of qutrits.
Superdense coding is a paradigmatic protocol in quantum information science, employing a quantum communication channel to send classical information more efficiently. As we show here, it can be understood as a particular case of a prepare and measure experiment, a scenario that has attracted growing attention for its fundamental and practical applications. Formulating superdense coding as a prepare and measure scenario allows us to provide a semi-device-independent witness of entanglement that significantly improves over previous tests. Furthermore, we also show how to adapt our results into s…
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…
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 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.
We introduce a general odd qubit entangled system composed of GHZ and Bell pairs and explicate its usefulness for quantum teleportation, information splitting and superdense coding. After demonstrating the superdense coding protocol on the five qubit system, we prove that '2N +1' classical bits can be sent by sending 'N+1' quantum bits using this channel. It is found that the five-qubit system is also ideal for arbitrary one qubit and two qubit teleportation and quantum information splitting (QIS). For the single qubit QIS, three different protocols are feasible, whereas for the two qubit QIS,…
Adopting quantum communication to modern networking requires transmitting quantum information through fiber-based infrastructure. We report the first demonstration of superdense coding over optical fiber links, taking advantage of a complete Bell-state measurement enabled by time-polarization hyperentanglement, linear optics, and common single-photon detectors. We demonstrate the highest single-qubit channel capacity to date utilizing linear optics, $1.665 \pm 0.018$, and we provide a full experimental implementation of a hybrid, quantum-classical communication protocol for image transfer.
We consider a task in which classical information is encoded into a quantum system by an operation restricted by symmetry. The maximum amount of classical information that can be encoded under this restriction, namely the symmetry-restricted classical information capacity, depends on the initial state of the system. Our focus is on whether the capacity of an asymmetric state can be strictly larger than that of any symmetric states, whereas the latter is a strictly positive constant. That is, we ask whether an analog of superdense coding is implementable in the resource theory of asymmetry. We …
We show that it is possible to transfer two-bit information via encoding a single qubit in a conventional nuclear magnetic resonance (NMR) experiment with two very weakly polarized nuclear spins. Nevertheless, the experiment can not be regarded as a demonstration of superdense coding by means of NMR because it is based on the large number of molecules being involved in the ensemble state rather than the entanglement of the NMR states. Following the discussions, an entanglement witness, particularly applicable for NMR, is introduced based on separate and simultaneous measurement of the individu…
Superdense coding uses entanglement as a resource to communicate classical information securely through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we have demonstrated a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary informat…
As we know, the states of triqubit systems have two important classes: GHZ-class and W-class. In this paper, the states of W-class are considered for teleportation and superdense coding, and are generalized to multi-particle systems. First we describe two transformations of the shared resources for teleportation and superdense coding, which allow many new protocols from some known ones for that. As an application of these transformations, we obtain a sufficient and necessary condition for a state of W-class being suitable for perfect teleportation and superdense coding. As another application,…
We study the performance of two measures of non-Markovianity in detecting memory effects in two-qubit dephasing channels. By combining independent Markovian and non-Markovian noise on the qubits, our results show that the trace distance measure is able to detect the memory effects when at least one of the local channels displays non-Markovianity. A measure based on channel capacity, in turn, becomes non-zero when the global two-qubit dynamics shows memory effects. We apply these schemes to a well-known superdense coding protocol and demonstrate an optimal noise configuration to maximize the in…
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.
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 show that with the fourpartite quantum channel used to teleport an arbitrary two qubit state, we can construct a superdense coding protocol where it is possible to transmit 4 bits of classical information sending only 2 qubits. Alice and Bob initially share a four qubit maximally entangled state and by locally manipulating her two qubits Alice can generate 16 orthogonal maximally entangled states, which are used to encode the message transmitted to Bob. He reads the 4 bit message by a generalized Bell state measurement. A generalized protocol in which 2N bits of classical information is tra…
Quantum superdense coding protocols enhance channel capacity by using shared quantum entanglement between two users. The channel capacity can be as high as 2 when one uses entangled qubits. However, this limit can be surpassed by using high-dimensional entanglement. We report an experiment that exceeds the limit using high-quality entangled ququarts with fidelities up to 0.98, demonstrating a channel capacity of $2.09\pm0.01$. The measured channel capacity is also higher than that obtained when transmitting only one ququart. We use the setup to transmit a five-color image with a fidelity of 0.…
A quantum secure direct communication network scheme is proposed with quantum superdense coding and decoy photons. The servers on a passive optical network prepare and measure the quantum signal, i.e., a sequence of the $d$-dimensional Bell states. After confirming the security of the photons received from the receiver, the sender codes his secret message on them directly. For preventing a dishonest server from eavesdropping, some decoy photons prepared by measuring one photon in the Bell states are used to replace some original photons. One of the users on the network can communicate any othe…
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.
By sending a classical two-level system, one can transfer information about only \emph{two} distinguishable outcomes. Here we show that in quantum mechanics, using both the spin and path degrees of freedom of a spin-1/2 particle, and a Mach-Zehnder type interferometric arrangement with two suitable Stern-Gerlach detectors, it is possible to transfer information about \emph{four} distinguishable outcomes. This procedure does \emph{not} require using quantum entanglement as a resource as in the well-known protocol of dense coding, but instead hinges entirely on the quantum superposition principl…
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 …
Quantum protocols require access to large-scale entangled quantum states, due to the requirement of channel capacity. As a promising candidate, the high-dimensional orbital angular momentum (OAM) entangled states have been implemented, but only one of four OAM Bell states in each individual subspace can be distinguished. Here we demonstrate the first realization of complete OAM Bell-state measurement (OAM-BSM) in an individual subspace, by seeking the suitable unitary matrix performable using only linear optics and breaking the degeneracy of four OAM Bell states in ancillary polarization dimen…
An interesting aspect of multipartite entanglement is that for perfect teleportation and superdense coding, not the maximally entangled W states but a special class of non-maximally entangled W-like states are required. Therefore, efficient preparation of such W-like states is of great importance in quantum communications, which has not been studied as much as the preparation of W states. In this letter, we propose a simple optical scheme for efficient preparation of large-scale polarization based entangled W-like states by fusing two W-like states or expanding a W-like state with an ancilla p…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of the algorithms, thereby decreasing any quantum advantage. Here we present a task-specific error-correction technique that provides a complete protection over a restricted set of quantum states. Specifically, we give an automated error correction in Superdense Coding algorithms utilizing n-qubit generalized Bell states. At its core, it is based on non-destructi…
The necessary and sufficient condition for perfect teleportation and superdense coding and all the suitable states for teleportation and superdense coding
We present a one-shot method for preparing pure entangled states between a sender and a receiver at a minimal cost of entanglement and quantum communication. In the case of preparing unentangled states, an earlier paper showed that a 2n-qubit quantum state could be communicated to a receiver by physically transmitting only n+o(n) qubits in addition to consuming n ebits of entanglement and some shared randomness. When the states to be prepared are entangled, we find that there is a reduction in the number of qubits that need to be transmitted, interpolating between no communication at all for m…
Dense coding is arguably the protocol that launched the field of quantum communication. Today, however, more than a decade after its initial experimental realization, the channel capacity remains fundamentally limited as conceived for photons using linear elements. Bob can only send to Alice three of four potential messages owing to the impossibility of carrying out the deterministic discrimination of all four Bell states with linear optics, reducing the attainable channel capacity from 2 to log_2 3 \approx 1.585 bits. However, entanglement in an extra degree of freedom enables the complete an…
Superdense coding promises increased classical capacity and communication security but this advantage may be undermined by noise in the quantum channel. We present a numerical study of how forward error correction (FEC) applied to the encoded classical message can be used to mitigate against quantum channel noise. By studying the bit error rate under different FEC codes, we identify the unique role that burst errors play in superdense coding, and we show how these can be mitigated against by interleaving the FEC codewords prior to transmission. We conclude that classical FEC with interleaving …
Many quantum information tasks rely on entanglement, which is used as a resource, for example, to enable efficient and secure communication. Typically, noise, accompanied by loss of entanglement, reduces the efficiency of quantum protocols. We develop and demonstrate experimentally a superdense coding scheme with noise, where the decrease of entanglement in Alice's encoding state does not reduce the efficiency of the information transmission. Having almost fully dephased classical two-photon polarization state at the time of encoding with concurrence $0.163\pm0.007$, we reach values of mutual …
Recently, Harrow et al. [Phys. Rev. Lett. 92, 187901 (2004)] gave a method for preparing an arbitrary quantum state with high success probability by physically transmitting some qubits, and by consuming a maximally entangled state, together with exhausting some shared random bits. In this paper, we discover that some states are impossible to be perfectly prepared by Alice and Bob initially sharing those entangled states that are superposed by the ground states, as the states to be prepared. In particular, we present a sufficient and necessary condition for the states being enabled to be exactl…
The complementarity of two observables is often captured in uncertainty relations, which quantify an inevitable tradeoff in knowledge. Here we study complementarity in the context of an information processing task: we link the complementarity of two observables to their usefulness for superdense coding (SDC). In SDC, Alice sends two classical dits of information to Bob by sending a single qudit. However, we show that encoding with commuting unitaries prevents Alice from sending more than one dit per qudit, implying that complementarity is necessary for SDC to be advantagous over a classical st…
Quantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac notation difficult to verify. This is why Coecke and Duncan have introduced a diagrammatic language for quantum protocols, called the ZX-calculus. This diagrammatic notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. In the author's MSc thesis it has been shown for over 25 quan…
The continuous-variable coherent (conat) channel is a useful resource for coherent communication, producing coherent teleportation and coherent superdense coding. We extend the conat channel to multiparty conditions by proposing definitions about multiparty position-quadrature conat channel and multiparty momentum-quadrature conat channel. We additionally provide two methods to implement this channel using linear optics. One method is the multiparty version of coherent communication assisted by entanglement and classical communication (CCAECC). The other is multiparty coherent superdense codin…
The coherent bit (cobit) channel is a resource intermediate between classical and quantum communication. It produces coherent versions of teleportation and superdense coding. We extend the cobit channel to continuous variables by providing a definition of the coherent nat (conat) channel. We construct several coherent protocols that use both a position-quadrature and a momentum-quadrature conat channel with finite squeezing. Finally, we show that the quality of squeezing diminishes through successive compositions of coherent teleportation and superdense coding.
We exhibit the intriguing phenomena of "Less is More" using a set of multipartite entangled states. We consider the quantum communication protocols for the {\em exact} teleportation, superdense coding, and quantum key distribution. We find that sometimes {\em less} entanglement is {\em more} useful. To understand this phenomena we obtain a condition that a resource state must satisfy to communicate a $n$-qubit pure state with $m$ terms. We find that the an appropriate partition of the resource state should have a von-Neumann entropy of ${\rm log}_{2} m$. Furthermore, it is shown that some stat…
The development of automated gate specification for quantum communications and quantum networked computation opens up the way for malware designed at corrupting the automation software, changing the automated quantum communications protocols and algorithms. We study two types of attacks on automated quantum communications protocols and simulate these attacks on the superdense coding protocol, using remote access to IBM's Quantum Computers available through IBM Q Experience to simulate these attacks on what would be a low noise quantum communications network. The first type of attack leads to a…
Utility of noiseless linear amplification and attenuation in single-rail discrete-variable quantum communications
University of Queensland（昆士兰大学）；The Australian National University（澳大利亚国立大学）；A*STAR Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局量子创新中心）；Q-CTRL
We present a quantum hyperdense coding protocol with hyperentanglement in polarization and spatial-mode degrees of freedom of photons first and then give the details for a quantum secure direct communication (QSDC) protocol based on this quantum hyperdense coding protocol. This QSDC protocol has the advantage of having a higher capacity than the quantum communication protocols with a qubit system. Compared with the QSDC protocol based on superdense coding with $d$-dimensional systems, this QSDC protocol is more feasible as the preparation of a high-dimension quantum system is more difficult th…
Some of the asymmetric three qubit $W$ states are used for perfect teleportation, superdense coding and quantum information splitting. We present the protocols for the optimal distillation of the asymmetric as well as the symmetric $W$ states from a single copy of any three qubit $W$ class pure state.
