Logical Bell Research Articles

Logical Bell state measurement for photon system in momentum and polarization degrees of freedom

Logical Bell state measurement for photon system in momentum and polarization degrees of freedom

Linear Optical Logical Bell State Measurements with Optimal Loss-Tolerance Threshold

Linear Optical Logical Bell State Measurements with Optimal Loss-Tolerance Threshold

Measurement-Device-Independent Quantum Key Distribution Based on Decoherence-Free Subspaces with Logical Bell State Analyzer.

Measurement-device-independent quantum key distribution (MDI-QKD) enables two legitimate users to generate shared information-theoretic secure keys with immunity to all detector side attacks. However, the original proposal using polarization encoding is sensitive to polarization rotations stemming from birefringence in fibers or misalignment. To overcome this problem, here we propose a robust QKD protocol without detector vulnerabilities based on decoherence-free subspaces using polarization-entangled photon pairs. A logical Bell state analyzer is designed specifically for such encoding. The protocol exploits common parametric down-conversion sources, for which we develop a MDI-decoy-state method, and requires neither complex measurements nor a shared reference frame. We have analyzed the practical security in detail and presented a numerical simulation under various parameter regimes, showing the feasibility of the logical Bell state analyzer along with the potential that double communication distance can be achieved without a shared reference frame.

Measurement-based logical qubit entanglement purification

Entanglement purification is the distilling of high-quality entanglement from low-quality entanglement and is a key element in the quantum repeater. As a new branch of entanglement purification, the measurement-based entanglement purification protocol (MBEPP) only requires one to perform the Bell state measurement to couple resource states with noisy pairs, and it tolerates more local noise than the conventional purification protocols. Existing MBEPPs usually focus on physical qubit entanglement. In this paper, we propose a measurement-based logical qubit entanglement purification protocol (MBLEPP) with quantum nondemolition detection (QND), where the qubit is encoded in the quantum parity code. The results show that this MBLEPP can also work with photon loss under the conditions that each block of the logical Bell state measurement contains at least one physical qubit, that at least one of the blocks is intact, and that the entanglement exists between all blocks. Moreover, we also consider the MBLEPP with imperfect QND. We show that below a certain QND error threshold, this MBLEPP can still work. In this way, this MBLEPP not only obtains high-fidelity entanglement but also tolerates photon loss and the error from imperfect QND. This MBLEPP combines the benefits of the MBEPP and quantum error correction code and may have potential application in long-distance quantum communication.

Error-correcting entanglement swapping using a practical logical photon encoding

Several emerging quantum technologies, including quantum networks, modular and fusion-based quantum computing, rely crucially on the ability to perform photonic Bell state measurements. Therefore, photon losses and the 50\% success probablity upper bound of Bell state measurements pose a critical limitation to photonic quantum technologies. Here, we develop protocols that overcome these two key challenges through logical encoding of photonic qubits. Our approach uses a tree graph state logical encoding, which can be produced deterministically with a few quantum emitters, and achieves near-deterministic logical photonic Bell state measurements while also protecting against errors including photon losses, with a record loss-tolerance threshold.

Development of Quantum Private Queries Protocol on Collective-Dephasing Noise Channel

Quantum private queries can commonly protect important information in a good many of domains, such as finance, business, military, which use quantum effects to achieve unprecedented classical private queries. However, quantum state can be easily affected by environmental noise, which affects the actual effect of quantum private queries. This paper developed a new quantum private query protocol based on four qubits logical Bell state to resist the collective-dephasing noise. The symmetric private information retrieval problem, which is the most influential problem in the process of quantum private query, was solved well by quantum oblivious transfer. It introduces the construction of four qubits logical Bell state. The quantum private query protocol innovates the quantum key distribution process by using the four qubits logical Bell state as the measurement base to measure the logical qubits, and ensures the function of quantum oblivious transmission. The protocol cannot only resist the noise influence of the communication process, but also ensure the security of both sides of the communication.

Two-party quantum key agreement against collective noisy channel

Quantum key agreement (QKA) permits participants to constitute a shared key on a quantum channel, and no participants are able to independently determine the shared key. In fact, particles are frequently affected by channel noise in the transmission process of quantum channel. Under the cover of noise, attackers can launch malicious attacks. In this thesis, on account of the usage of entanglement swapping of GHZ state and logical Bell states, we design two two-party QKA protocols which are immune to collective-dephasing noise and collective-rotation noise, respectively. In comparison with the existing QKA protocols of two parties, the proposed protocols have better quantum resource cost and the qubit efficiency in the global scope. Security analysis reveals that they can resist not only attacks by participants but also external attacks.

Cryptanalysis and improvement of the robust quantum dialogue protocols based on the entanglement swapping between any two logical Bell states and the shared auxiliary logical Bell state

As we know, it does not allow that a secure quantum communication protocol has the information leakage problem. Unfortunately, we find that there is the information leakage problem in the two quantum dialogue (QD) protocols which are respectively based on entanglement swapping between two logical Bell states under the collective-dephasing noise and the collective-rotation noise. To mend this loophole, they are masterly improved. It is proven that the improved QD protocols are without information leakage problem. Incidentally, they have some other obvious advantages compared to the previous ones.

Efficiencies of logical Bell measurements on Calderbank-Shor-Steane codes with static linear optics

We show how the efficiency of a logical Bell measurement (BM) can be calculated for arbitrary CSS codes with the experimentally important constraint of using only transversal static linear-optical BMs on the physical single-photon qubit level. For this purpose, we utilize the codes' description in terms of stabilizers in order to calculate general efficiencies for the loss-free case, but also for specific cases including photon loss. These efficiencies can be, for instance, used for obtaining transmission rates of all-optical quantum repeaters. In the loss-free case, we demonstrate that the important class of CSS codes with identical physical-qubit support for the two logical Pauli ($Z$ and $X$) operators can only achieve a logical BM efficiency of $\frac{1}{2}$ if one always employs the same ancilla-free static linear optical BMs on the physical level. We apply our methods to various CSS codes including two-dimensional planar color and planar surface codes. We then find that in many cases, the fixed use of the standard linear optical BM for all physical BMs is suboptimal and performing linear optical transformations before doing the standard linear optical BM (still without any ancillary photons and without any feedforward) can increase the efficiency enormously. In fact, using this generalization in the no-loss (or sometimes also in the low-loss) case allows us, on the one hand, to improve the logical BM efficiency of quantum parity codes compared to previously known results and, on the other hand, it also enables us to enhance the efficiency of two-dimensional planar color codes, whose efficiency is otherwise subject to the above $\frac{1}{2}$ bound, to arbitrarily close to unity.

Stronger Hardy-type paradox based on the Bell inequality and its experimental test

Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as ``the simplest form of Bell's theorem.'' In this work, we advance the study of Hardy's paradox based on Bell's inequality. Our formalism is essentially equivalent to the ``logical Bell inequality'' formalism developed by Abramsky and Hardy, but ours is more easily applied to experimental tests. Remarkably, we find that not only for a two-qubit two-setting case but also for a two-qubit four-setting case, we can construct stronger Hardy-type paradoxes based on Bell's inequality, whose successful probabilities can attain four times and seven times larger than the original one, respectively, thus providing more friendly tests for experiment. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.

Two-party quantum key agreement over a collective noisy channel

Quantum key agreement (QKA) allows participants to establish a shared key over a quantum channel, and no one of the participants can determine the shared key alone. Actually, particles are usually affected by noise during transmission in the quantum channel, and an aggressor can launch a baleful attack under the cover of noise. In this paper, based on logical Bell states, we propose two robust two-party QKA protocols immune to collective-dephasing noise and collective-rotation noise, respectively. The measurement correlation of quantum entanglement is utilized to establish a shared key. The proposed protocols are globally better in terms of quantum resource cost and qubit efficiency than existing two-party QKA protocols against collective noise. The security analysis demonstrates that they can resist common insider and outsider attacks.

Reference-frame-independent measurement-device-independent quantum key distribution using hybrid logical basis

The multiple-qubit logical basis, originally introduced in the context of fault-tolerant quantum computing in decoherence-free subspace (DFS), has specific applications for resolving a reference frame misalignment problem in quantum information protocols. In this paper, an alignment-free MDI-QKD scheme is proposed with rotational-invariant state, which is immune to the collective noise induced by misalignment between two distant legitimate parties. In our protocol, the initial logical qubit is created in the polarization-orbit angular momentum hybrid space, while the transmission is entirely done in the rotation-invariant DFS under the collective noise associated with misalignment. The partial Bell state measurement is performed on the logical qubits to sort the logical Bell state. Compared with the original MDI-QKD protocols, the numerical simulations show that our modified scheme has apparent improvements both in transmission distance and key generation rate. Furthermore, only ordinary optical elements are required in our protocol.

Multi-server blind quantum computation over collective-noise channels

Blind quantum computation (BQC) enables ordinary clients to securely outsource their computation task to costly quantum servers. Besides two essential properties, namely correctness and blindness, practical BQC protocols also should make clients as classical as possible and tolerate faults from nonideal quantum channel. In this paper, using logical Bell states as quantum resource, we propose multi-server BQC protocols over collective-dephasing noise channel and collective-rotation noise channel, respectively. The proposed protocols permit completely or almost classical client, meet the correctness and blindness requirements of BQC protocol, and are typically practical BQC protocols.

Two robust quantum key agreement protocols based on logical GHZ states

Based on logical GHZ states and logical Bell states, two robust quantum key agreement protocols are proposed, which can be immune to the collective-dephasing noise and the collective-rotation noise, respectively. The delayed measurement technique ensures that two participants can fairly negotiate a shared key and any one of them cannot successfully perform the participant attacks. The two protocols are congenitally free from the Trojan horse attacks and they can resist against other outsider attacks with the help of the decoy state technology. Moreover, they have no information leakage problem and achieve high qubit efficiency.

Two-party quantum key agreement against collective noise

In this paper, two two-party quantum key agreement protocols are proposed with logical $$\chi $$ź-states and logical Bell states. These two protocols can be immune to the collective-dephasing noise and the collective-rotation noise, respectively. They make full use of the measurement correlation property of multi-particle entangled states and the delayed measurement technique. This ensures that two participants can exchange the secret keys of each other and fairly establishes a shared key. There is no information leakage problem when establishing a shared key. The use of the delayed measurement technique and the decoy state technology makes the two protocols resist against both participant and outsider attacks. Furthermore, the two protocols are congenitally free from the Trojan horse attacks and have high qubit efficiency.

Fault-tolerant quantum blind signature protocols against collective noise

This work proposes two fault-tolerant quantum blind signature protocols based on the entanglement swapping of logical Bell states, which are robust against two kinds of collective noises: the collective-dephasing noise and the collective-rotation noise, respectively. Both of the quantum blind signature protocols are constructed from four-qubit decoherence-free (DF) states, i.e., logical Bell qubits. The initial message is encoded on the logical Bell qubits with logical unitary operations, which will not destroy the anti-noise trait of the logical Bell qubits. Based on the fundamental property of quantum entanglement swapping, the receiver simply performs two Bell-state measurements (rather than four-qubit joint measurements) on the logical Bell qubits to verify the signature, which makes the protocols more convenient in a practical application. Different from the existing quantum signature protocols, our protocols can offer the high fidelity of quantum communication with the employment of logical qubits. Moreover, we hereinafter prove the security of the protocols against some individual eavesdropping attacks, and we show that our protocols have the characteristics of unforgeability, undeniability and blindness.

Interoperability in encoded quantum repeater networks

The future of quantum repeater networking will require interoperability between various error correcting codes. A few specific code conversions and even a generalized method are known, however, no detailed analysis of these techniques in the context of quantum networking has been performed. In this paper, we analyze a generalized procedure to create Bell pairs encoded heterogeneously between two separate codes used often in error corrected quantum repeater network designs. We begin with a physical Bell pair, then encode each qubit in a different error correcting code, using entanglement purification to increase the fidelity. We investigate three separate protocols for preparing the purified encoded Bell pair. We calculate the error probability of those schemes between the Steane [[7,1,3]] code, a distance three surface code and single physical qubits by Monte Carlo simulation under a standard Pauli error model, and estimate the resource efficiency of the procedures. A local gate error rate of $10^{-3}$ allows us to create high-fidelity logical Bell pairs between any of our chosen codes. We find that a postselected model, where any detected parity flips in code stabilizers result in a restart of the protocol, performs the best.

Faithful deterministic secure quantum communication and authentication protocol based on hyperentanglement against collective noise**Project supported by the National Natural Science Foundation of China (Grant No. 61402058), the Science and Technology Support Project of Sichuan Province, China (Grant No. 2013GZX0137), the Fund for Young Persons Project of Sichuan Province, China (Grant No. 12ZB017), and the Foundation of Cyberspace Security Key Laboratory

Higher channel capacity and security are difficult to reach in a noisy channel. The loss of photons and the distortion of the qubit state are caused by noise. To solve these problems, in our study, a hyperentangled Bell state is used to design faithful deterministic secure quantum communication and authentication protocol over collective-rotation and collective-dephasing noisy channel, which doubles the channel capacity compared with using an ordinary Bell state as a carrier; a logical hyperentangled Bell state immune to collective-rotation and collective-dephasing noise is constructed. The secret message is divided into several parts to transmit, however the identity strings of Alice and Bob are reused. Unitary operations are not used.

Fault-tolerant authenticated quantum dialogue using logical Bell states

Two fault tolerant authenticated quantum dialogue (AQD) protocols are proposed in this paper by employing logical Bell states as the quantum resource, which combat the collective-dephasing noise and the collective-rotation noise, respectively. The two proposed protocols each can accomplish the mutual identity authentication and the dialogue between two participants simultaneously and securely over one kind of collective noise channels. In each of two proposed protocols, the information transmitted through the classical channel is assumed to be eavesdroppable and modifiable. The key for choosing the measurement bases of sample logical qubits is pre-shared privately between two participants. The Bell state measurements rather than the four-qubit joint measurements are adopted for decoding. The two participants share the initial states of message logical Bell states with resort to the direct transmission of auxiliary logical Bell states so that the information leakage problem is avoided. The impersonation attack, the man-in-the-middle attack, the modification attack and the Trojan horse attacks from Eve all are detectable.

QUANTUM TEAM LOGIC AND BELL’S INEQUALITIES

AbstractA logical approach to Bell’s Inequalities of quantum mechanics has been introduced by Abramsky and Hardy (Abramsky & Hardy, 2012). We point out that the logical Bell’s Inequalities of Abramsky & Hardy (2012) are provable in the probability logic of Fagin, Halpern and Megiddo (Fagin et al., 1990). Since it is now considered empirically established that quantum mechanics violates Bell’s Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell’s Inequalities are not provable, and prove a Completeness theorem for this logic. For this end we generalise the team semantics of dependence logic (Väänänen, 2007) first to probabilistic team semantics, and then to what we call quantum team semantics.