Two-way Classical Communication Research Articles

Side-Channel-Secure Quantum Key Distribution with Imperfect Vacuum Sources

The side-channel-secure (SCS) quantum key distribution (QKD), SCS QKD has attracted much attention due to its higher security compared to the measurement-device-independent protocols. It is not only measurement-device-independent secure, but also secure against source-state side channels provided that Eve has no access to Alice's or Bob's setups inside their labs. In the original protocol for SCS QKD, the side channels and the intensities of the coherent sources are allowed to be different in different time windows, but the vacuum sources of Alice and Bob have to be perfect, which is impossible in practice due to the finite extinction ratio of the intensity modulators. In this paper, we present a method that does not need the perfect vacuum source requested by the original protocol and assures the result as secure as the original protocol. With the upper bounds of the amplitudes of the nonvacuum part of the sources, the secure key rate of our SCS QKD protocol here with imperfect vacuum and unstable sources can be calculated. The numerical results show that, the secure distance of the SCS QKD protocol exceeds 150 km, provided that the intensity of the imperfect vacuum source is less than ${10}^{\ensuremath{-}8}$, which can be achieved in the experiment by a two-stage intensity modulator, where we also show that the active odd-parity pairing method and standard pairing method using two-way classical communication can be applied to the SCS QKD protocol to improve the key rate. Given the side-channel security based on the existing technological level, this work makes it possible to realize side-channel-secure QKD with real devices.

Simultaneous two-way classical communication and measurement-device-independent quantum key distribution on oceanic quantum channels

Simultaneous two-way classical and quantum (STCQ) communication combines both continuous classical coherent optical communication and continuous-variable quantum key distribution (CV-QKD), which eliminates all detection-related imperfections by being measurement-device-independent (MDI). In this paper, we propose a protocol relying on STCQ communication on the oceanic quantum channel, in which the superposition-modulation-based coherent states depend on the information bits of both the secret key and the classical communication ciphertext. We analyse the encoding combination in classical communication and consider the probability distribution transmittance under seawater turbulence with various interference factors. Our numerical simulations of various practical scenarios demonstrate that the proposed protocol can simultaneously enable two-way classical communication and CV-MDI QKD with just a slight performance degradation transmission distance compared to the original CV-MDI QKD scheme. Moreover, the asymmetric situation outperforms the symmetric case in terms of transmission distance and optical modulation variance. We further take into consideration the impact of finite-size effects to illustrate the applicability of the proposed scheme in practical scenarios. The results show the feasibility of the underwater STCQ scheme, which contributes toward developing a global quantum communication network in free space.

Quantum versus Randomized Communication Complexity, with Efficient Players

We study a new type of separations between quantum and classical communication complexity, separations that are obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits, with oracle access to their inputs. Our main result qualitatively matches the strongest known separation between quantum and classical communication complexity Gavinsky (2016) and is obtained using a quantum protocol where all parties are efficient. More precisely, we give an explicit partial Boolean function f over inputs of length N, such that: Items (1), (2) qualitatively match the strongest known separation between quantum and classical communication complexity, proved by Gavinsky (2016). Item (3) is new. (Our result is incomparable to the one of Gavinsky. While he obtained a quantitatively better lower bound of $$\Omega\left(N^{1/2}\right)$$ in the classical case, the referee in his quantum protocol is inefficient). Exponential separations of quantum and classical communication complexity have been studied in numerous previous works, but to the best of our knowledge the efficiency of the parties in the quantum protocol has not been addressed, and in most previous separations the quantum parties seem to be inefficient. The only separations that we know of that have efficient quantum parties are the recent separations that are based on lifting Göös et al. (2017), Chattopadhyay et al. (2019a). However, these separations seem to require quantum protocols with at least two rounds of communication, so they imply a separation of two-way quantum and classical communication complexity, but they do not give the stronger separations of simultaneous-message quantum communication complexity vs. two-way classical communication complexity (or even one-way quantum communication complexity vs. two-way classical communication complexity). Our proof technique is completely new, in the context of communication complexity, and is based on techniques from Raz & Tal (2019). Our function f is based on a lift of the forrelation problem, using xor as a gadget.

Robust twin-field quantum key distribution through sending or not sending.

The sending-or-not-sending (SNS) protocol is one of the most major variants of the twin-field (TF) quantum key distribution (QKD) protocol and has been realized in a 511-km field fiber, the farthest field experiment to date. In practice, however, all decoy-state methods have unavoidable source errors, and the source errors may be non-random, which compromises the security condition of the existing TF-QKD protocols. In this study, we present a general approach for efficiently calculating the SNS protocol's secure key rate with source errors, by establishing the equivalent protocols through virtual attenuation and the tagged model. This makes the first result for TF QKD in practice where source intensity cannot be controlled exactly. Our method can be combined with the two-way classical communication method such as active odd-parity pairing to further improve the key rate. The numerical results show that if the intensity error is within a few percent, the key rate and secure distance only decrease marginally. The key rate of the recent SNS experiment in the 511-km field fiber is still positive using our method presented here, even if there is a [Formula: see text] intensity fluctuation. This shows that the SNS protocol is robust against source errors.

Rate limits in quantum networks with lossy repeaters

The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, we model the loss introduced at the repeater stations and then prove the corresponding limits. In the linear chain scenario we show that, by increasing the number of repeater stations, the maximum rate cannot overcome a quantity which solely depends on the loss of a single station. We introduce a way of adapting the standard machinery for obtaining bounds to this realistic scenario. The difference is that whilst ultimate limits for any strategy can be derived given a fixed channel, when the repeaters introduce additional decoherence, then the effective overall channel is itself a function of the chosen repeater strategy (e.g., one-way versus two-way classical communication). Classes of repeater strategies can be analysed using additional modelling and the subsequent bounds can be interpreted as the optimal rate within that class.

Single-Shot Secure Quantum Network Coding for General Multiple Unicast Network With Free One-Way Public Communication

It is natural in a quantum network system that multiple users intend to send their quantum message to their respective receivers, which is called a multiple unicast quantum network. We propose a canonical method to derive a secure quantum network code over a multiple unicast quantum network from a secure classical network code. Our code correctly transmits quantum states when there is no attack. It also guarantees the secrecy of the transmitted quantum state even with the existence of an attack when the attack satisfies a certain natural condition. In our security proof, the eavesdropper is allowed to modify wiretapped information dependently on the previously wiretapped messages. Our protocol guarantees the secrecy by utilizing one-way classical information transmission (public communication) in the same direction as the quantum network although the verification of quantum information transmission requires two-way classical communication. In the protocol, some nodes may share secret randomness as resources in advance. Our secure network code can be applied to several networks including the butterfly network.

Composable security for practical quantum key distribution with two way classical communication

We present a theory for the composable security of sending-or-not-sending (SNS) protocol of twin field quantum key distribution (TF-QKD). We present methods to strictly calculate the finite-key effects in QKD with error rejection through two-way classical communication (TWCC) for SNS TF-QKD protocol. Unlike the normal QKD without TWCC, here the probability of tagging or untagging for each two-bit random group is not independent. We rigorously solve this problem by imagining a virtual set of bits where every bit is independent and identical. With explicit formulas, we show that simply applying Chernoff bound in the calculation gives correct key rate, but the failure probability changes a little bit. We calculate the key rate with strict bounds and security, and obtain key rates by far breaking the PLOB (Pirandola, Laurenza, Ottaviani, and Banchi) bound with composable security.

Quantum one-way versus classical two-way communication in XOR games

In this work, we give an example of exponential separation between quantum and classical resources in the setting of XOR games assisted with communication. Specifically, we show an example of a XOR game for which O(n) bits of two-way classical communication are needed in order to achieve the same value as can be attained with $$\log n$$ qubits of one-way communication. We also find a characterization for the value of a XOR game assisted with a limited amount of two-way communication in terms of tensor norms of normed spaces.

Locally distinguishable maximally entangled states by two-way LOCC

We concentrate on the differences between one-way local operations and classical communication (1-LOCC) and two-way local operations and classical communication (2-LOCC) in distinguishing maximally entangled states (MESs). We analyze the 2-LOCC distinguishability of k MESs which were constructed by using 1-LOCC indistinguishable qubit lattice states (LSs) (Nathanson in Phys Rev A 88:062316, 2013). We give a sufficient condition that illustrates which type of Nathanson’s constructed states can be distinguished by 2-LOCC. It partly solves an open question proposed by Nathanson. Furthermore, we answer the question in a simpler and more efficient way, at least to some extent. That is, the k constructed states can be distinguished by 2-LOCC but not by 1-LOCC if $$k(k-1)-m(m-1)< 2^{r+2}$$ , where the initial LSs are in $${\mathbb {C}}^{2^{r}}\otimes {\mathbb {C}}^{2^{r}}$$ and m is the largest number of pairwise commuting matrices corresponding to the initial LSs. Finally, we find an interesting phenomenon, i.e., 1-LOCC and 2-LOCC work differently when distinguishing four ququad-ququad LSs and distinguishing four constructed states derived from the four LSs. For the four ququad-ququad LSs, 2-LOCC has no advantage over 1-LOCC. However, for the four constructed states, 2-LOCC has advantages over 1-LOCC.

General upper bound for conferencing keys in arbitrary quantum networks

Secure quantum conferencing refers to a protocol where a number of trusted users generate exactly the same secret key to confidentially broadcast private messages. By a modification of the techniques first introduced in [Pirandola, arXiv:1601.00966], we derive a single-letter upper bound for the maximal rates of secure conferencing in a quantum network with arbitrary topology, where the users are allowed to perform the most powerful local operations assisted by two-way classical communications, and the quantum systems are routed according to the most efficient multipath flooding strategies. More precisely, our analysis allows us to bound the ultimate rates that are achievable by single-message multiple-multicast protocols, where N senders distribute N independent secret keys, and each key is to be shared with an ensemble of M receivers.

Assisted concentration of Gaussian resources

In spite of their outstanding experimental relevance, Gaussian operations in continuous-variable quantum systems are subjected to fundamental limitations, as it is known that general resources cannot be distilled within the Gaussian paradigm. We show that these limitations can be overcome by considering a collaborative setting where one party increases the amount of local resource with the aid of another party, whose operations are assumed to be Gaussian but are otherwise unrestricted; the two parties can only communicate classically. We show that in single-shot scenarios, unlike in the well-known case of entanglement theory, two-way classical communication does not lead to any improvement over one-way classical communication from the aiding party to the aided party. We then provide a concise general expression for the Gaussian resource of assistance, i.e., the maximum amount of resource that can be obtained when the aiding party holds a purification of the aided party's state, as measured by a general monotone. To demonstrate its usefulness, we apply our result to two important kinds of resources, squeezing and entanglement, and find some simple analytic solutions. In the case of entanglement theory, we are able to find general upper bounds on the regularized Gaussian entanglement of assistance, and to establish additivity for tensor powers of thermal states. This allows us to draw a quantitative and enlightening comparison with the performance of assisted entanglement distillation in the non-Gaussian setting. On the technical side, we develop some variational expressions to handle functions of symplectic eigenvalues that may be of independent interest. Our results suggest further potential for Gaussian operations to play a major role in practical quantum information processing protocols.

Simple communication complexity separation from quantum state antidistinguishability

A set of $n$ pure quantum states is called antidististinguishable if there exists an $n$-outcome measurement that never outputs the outcome `$k$' on the $k$-th quantum state. We describe sets of quantum states for which any subset of three states is antidistinguishable and use this to produce a two-player communication task that can be solved with $\log d$ qubits, but requires one-way communication of at least $\log (4/3) (d-1) - 1 \approx 0.415 (d-1) - 1$ classical bits. The advantages of the approach are that the proof is simple and self-contained -- not needing, for example, to rely on hard-to-establish prior results in combinatorics -- and that with slight modifications, non-trivial bounds can be established in any dimension $\geq 3$. The task can be framed in terms of the separated parties solving a relation, and the separation is also robust to multiplicative error in the output probabilities. We show, however, that for this particular task, the separation disappears if two-way classical communication is allowed. Finally, we state a conjecture regarding antidistinguishability of sets of states, and provide some supporting numerical evidence. If the conjecture holds, then there is a two-player communication task that can be solved with $\log d$ qubits, but requires one-way communication of $\Omega (d \log d)$ classical bits.

Simultaneous two-way classical communication and measurement-device-independent quantum key distribution with coherent states

Simultaneous quantum and classical communication integrates both continuous variable quantum key distribution and classical coherent optical communication by using the same communication infrastructure. Given its compelling benefits, we proposed a protocol relying on both two-way classical communication and on measurement-device-independent quantum key distribution, in which the superposition-modulation-based coherent states depend on the information bits of both the secret key and on the classical communication ciphertext, which are measured by an untrusted relay node. The proposed scheme strikes a beneficial balance between its level of security and its grade of practicability. Explicitly, on the one hand, the secret key obtained is secure against all attacks on the detectors, and it is eminently suitable for bidirectional classical communication in the metropolitan network as a benefit of its relay-based configuration. Our results show a convincing bit error rate vs secret key rate trade-off for transmission over dozens of kilometers in the quantum channel, hence striking an excellent integrity (bit error rate) vs security trade-off.

Optimal verification of general bipartite pure states

The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

State-independent quantum key distribution with two-way classical communication

A quantum key distribution protocol is proposed that is a variation of BB84 that provides raw key generation from correlations that violate a Bell-type inequality for single qubit systems and not entangled pairs. Additionally, it 1) is state-independent, 2) involves two-way classical communication, and 3) does not require basis matching between the two parties. The Brukner-Taylor-Cheung-Vedral (BTCV) time-like form of the Bell-CHSH inequality by Bruk and by Tay is employed as an eavesdropping check; sequential measurements lead to an inequality identical in form to the Bell-CHSH inequality, which relies only on the measurements performed with no regard for the qubit states. We show that this form manifests naturally from the non-commutativity of observables.

Coherent-State-Based Twin-Field Quantum Key Distribution

Large-scale quantum communication networks are still a huge challenge due to the rate-distance limit of quantum key distribution (QKD). Recently, twin-field (TF) QKD has been proposed to overcome this limit. Here, we prove that coherent-state-based TF-QKD is a time-reversed entanglement protocol, where the entanglement generation is realized with entanglement swapping operation via an entangled coherent state measurement. We propose a coherent-state-based TF-QKD with optimal secret key rate under symmetric and asymmetric channels by using coherent state and cat state coding. Furthermore, we show that our protocol can be converted to all recent coherent-state-based TF-QKD protocols by using our security proof. By using the entanglement purification with two-way classical communication, we improve the transmission distance of all coherent-state-based TF-QKD protocols.

Optimal verification of two-qubit pure states

In a recent work [Phys. Rev. Lett. 120, 170502 (2018)], Pallister et al. proposed an optimal strategy to verify non-maximally entangled two-qubit pure states under the constraint that the accessible measurements being locally projective and non-adaptive. Their nice result leads naturally to the question: What is the optimal strategy among general LOCC measurements? In this Letter, we answer this problem completely for two-qubit pure states. To be specific, we give the optimal strategy for each of the following available classes of measurements: (i) local operations and one-way classical communication (one-way LOCC) measurements; (ii) local operations and two-way classical communication (two-way LOCC) measurements; and (iii) separable measurements. Surprisingly, our results reveal that for the two-qubit pure state verification problem, two-way LOCC measurements remarkably outperforms one-way LOCC measurements and has the same power as the separable measurements.

Improving the lower bound to the secret-key capacity of the thermal amplifier channel

We consider the noisy thermal amplifier channel, where signal modes are amplified together with environmental thermal modes. We focus on the secret-key capacity of this channel, which is the maximum amount of secret bits that two remote parties can generate by means of the most general adaptive protocol, assisted by unlimited and two-way classical communication. For this channel only upper and lower bounds are known, and in this work we improve the lower bound. We consider a protocol based on squeezed states and homodyne detections, in both direct and reverse reconciliation. In particular, we assume that trusted thermal noise is mixed on beam splitters controlled by the parties in a way to assist their homodyne detections. The new improved lower bounds to the secret-key capacity are obtained by optimizing the key rates over the variance of the trusted noise injected, and the transmissivity of the parties’ beam splitters. Our results confirm that there is a separation between the coherent information of the thermal amplifier channel and its secret key capacity.Graphical abstract

Efficient Teleportation for High-Dimensional Quantum Computing

Performance of an entangled quantum channel is affected by classical feedback assisted in quantum communications. For example, in quantum-gate teleportation schemes, the capacity of an independent entangled quantum channel is reduced by utilizing two-way simultaneous classical communication (TWSCC↔). However, by exploiting the superposition of high-dimensional quantum channels, the transmission efficiency of the quantum-gate teleportation can be dramatically improved with TWSCC↔. In this study, we investigate the possibility of achieving an efficient scheme of nonlocal high-dimensional quantum computation by using hyperentangled photon pairs, atoms, and an optical micro-resonator coupled system. The feasibility and efficiency of the scheme are also discussed. Results prove that, for nonlocal quantum computing, high-dimensional quantum operation performs better than traditional methods that decompose the high-dimensional Hilbert space into two-dimensional quantum space under limited prior shared maximally entangled resources.

Quantum Enhancement of Randomness Distribution

The capability of a given channel to communicate information is, a priori, distinct from its capability to distribute shared randomness. In this article we define randomness distribution capacities of quantum channels assisted by forward, back, or two-way classical communication and compare these to the corresponding communication capacities. With forward assistance or no assistance, we find that they are equal. We establish the mutual information of the channel as an upper bound on the two-way assisted randomness distribution capacity. This implies that all of the capacities are equal for classical-quantum channels. On the other hand, we show that the back-assisted randomness distribution capacity of a quantum-classical channels is equal to its mutual information. This is often strictly greater than the back-assisted communication capacity. We give an explicit example of such a separation where the randomness distribution protocol is noiseless.