Entanglement Assistance Research Articles

Entanglement-assisted Quantum Reed-Muller Tensor Product Codes

We present the construction of standard entanglement-assisted (EA) qubit Reed-Muller (RM) codes and their tensor product variants from classical RM codes. We show that the EA RM codes obtained using the CSS construction have zero coding rate and negative catalytic rate. We further show that EA codes constructed from these same classical RM codes using the tensor product code (TPC) construction have positive coding rate and provide a subclass of EA RM TPCs that have positive catalytic rate, thus establishing the coding analog of superadditivity for this family of codes, useful towards quantum communications. We also generalize this analysis to obtain conditions for EA TPCs from classical codes to have positive catalytic rate when their corresponding EA CSS codes have zero rate.

Experimental sharing of Bell nonlocality with projective measurements

In the standard Bell experiment, two parties perform local projective measurements on a shared pair of entangled qubits to generate nonlocal correlations. However, these measurements completely destroy the entanglement, rendering the post-measurement state unable for subsequent use. For a long time, it was believed that only unsharp measurements can be used to share quantum correlations. Remarkably, recent research has shown that classical randomness assisted projective measurements are sufficient for sharing nonlocality (Steffinlongo and Tavakoli 2022 Phys. Rev. Lett. 129 230402). Here, by stochastically combining no more than two different projective measurement strategies, we report an experimental observation of double Clauser–Horne–Shimony–Holt inequality violations with two measurements in a sequence made on each pair of maximally and partially entangled polarization photons. Our results reveal that the double violation achieved by partially entangled states can be 11 standard deviations larger than that achieved by maximally entangled ones. Our scheme eliminates the requirement for entanglement assistance in previous unsharp-measurement-based sharing schemes, making it experimentally easier. Our work provides possibilities for sharing other types of quantum correlations in various physical systems with projective measurements.

Entanglement assisted communication over the free-space optical link with azimuthal phase correction for atmospheric turbulence by adaptive optics.

To improve the reliability of entanglement-assisted (EA) communication over turbulent FSO channels we propose to perform the optical phase-conjugation on idler photons rather than turbulence affected signal photons and use adaptive optics. We experimentally demonstrate that reliable EA communication over outdoor 1.45 km FSO link, established at University of Arizona campus, is possible in strong turbulence regime.

Communication over entanglement-breaking channels with unreliable entanglement assistance

Communication over entanglement-breaking channels with unreliable entanglement assistance

More assistance of entanglement, less rounds of classical communication

Classical communication plays a crucial role to distinguish locally a class of quantum states. Despite considerable advances, we have very little knowledge about the number of measurement and communication rounds needed to implement a discrimination task by local quantum operations and classical communications (in short, LOCC). In this paper, we are able to show the relation between round numbers with the local discrimination of a set of pure bipartite orthogonal quantum states. To demonstrate the possible strong dependence on the round numbers, we consider a class of orthogonal product states in , which require at least round of classical communications. Curiously the round number can be reduced to d by the assistance of one-ebit of entanglement as resource and can be reduced further by assistance of more entanglement. We are also able to show that the number of LOCC rounds needed for a discrimination task may depend on the amount of entanglement assistance.

Communication With Unreliable Entanglement Assistance

Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. In order to generate entanglement for optical communication, the transmitter and the receiver first prepare entangled spin-photon pairs locally, and then the photon at the transmitter is sent to the receiver through an optical fiber or free space. Without feedback, the transmitter does not know whether the entangled photon has reached the receiver. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance. It is further established that time division between entanglement-assisted and unassisted coding strategies is optimal for the noiseless qubit channel, but can be strictly suboptimal for a noisy channel.

Ultimate precision limit of noise sensing and dark matter search

The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a “nulling” measurement (squeezing and photon counting) to achieve the optimal performances. In terms of the scan rate, even with 20-decibel of strength, single-mode squeezing still underperforms the vacuum limit which is achieved by photon counting on vacuum input; while the two-mode squeezed vacuum provides large and close-to-optimum advantage over the vacuum limit, thus more exotic quantum resources are no longer required. Our results highlight the necessity of entanglement assistance and microwave photon counting in dark matter search.

Quantum optical communication in the presence of strong attenuation noise

Is quantum communication possible over an optical fibre with transmissivity $\lambda\leq 1/2$ ? The answer is well known to be negative if the environment with which the incoming signal interacts is initialised in a thermal state. However, in [PRL 125:110504, 2020] the quantum capacity was found to be always bounded away from zero for all $\lambda>0$, a phenomenon dubbed "die-hard quantum communication" (D-HQCOM), provided that the initial environment state can be chosen appropriately (depending on $\lambda$). Here we show an even stronger version of D-HQCOM in the context of entanglement-assisted classical communication: entanglement assistance and control of the environment enable communication with performance at least equal to that of the ideal case of absence of noise, even if $\lambda>0$ is arbitrarily small. These two phenomena of D-HQCOM have technological potential provided that we are able to control the environment. How can we achieve this? Our second main result answers this question. Here we provide a fully consistent protocol to activate the phenomena of D-HQCOM without directly accessing the environment state. This is done by sending over the channel "trigger signals", i.e. signals which do not encode information, prior to the actual communication, with the goal of modifying the environment in an advantageous way. This is possible thanks to the memory effects which arise when the sender feeds signals separated by a sufficiently short temporal interval. Our results may offer a concrete scheme to communicate across arbitrarily long optical fibres, without using quantum repeaters. As a by-product of our analysis, we derive a simple Kraus representation of the thermal attenuator exploiting the associated Lindblad master equation.

On Entanglement-Assisted Multistatic Radar Techniques.

Entanglement-based quantum sensors have much better sensitivity than corresponding classical sensors in a noisy and lossy regime. In our recent paper, we showed that the entanglement-assisted (EA) joint monostatic–bistatic quantum radar performs much better than conventional radars. Here, we propose an entanglement-assisted (EA) multistatic radar that significantly outperforms EA bistatic, coherent state-based quantum, and classical radars. The proposed EA multistatic radar employs multiple entangled transmitters performing transmit-side optical phase conjugation, multiple coherent detection-based receivers serving as EA detectors, and a joint detector.

Entanglement in prepare-and-measure scenarios: many questions, a few answers

Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure (PM) scenarios in the last decade. Here, we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focussing on entanglement-assisted (EA) PM scenarios. In a recent companion paper (arXiv:2103.10748), we investigated correlations based on unrestricted entanglement. Here, our focus is on scenarios with restricted entanglement. We establish several elementary relations between standard classical and quantum communication and their EA counterparts. In particular, while it was already known that bits or qubits assisted by two-qubit entanglement between the sender and receiver constitute a stronger resource than bare bits or qubits, we show that higher-dimensional entanglement further enhance the power of bits or qubits. We also provide a characterisation of generalised dense coding protocols, a natural subset of EA quantum communication protocols, finding that they can be understood as standard quantum communication protocols in real-valued Hilbert space. Though such dense coding protocols can convey up to two bits of information, we provide evidence, perhaps counter-intuitively, that resources with a small information capacity, such as a bare qutrits, can sometimes produce stronger correlations. Along the way we leave several conjectures and conclude with a list of interesting open problems.

Entanglement-Assisted Joint Monostatic-Bistatic Radars.

With the help of entanglement, we can build quantum sensors with sensitivity better than that of classical sensors. In this paper we propose an entanglement assisted (EA) joint monostatic-bistatic quantum radar scheme, which significantly outperforms corresponding conventional radars. The proposed joint monostatic-bistatic quantum radar is composed of two radars, one having both wideband entangled source and EA detector, and the second one with only an EA detector. The optical phase conjugation (OPC) is applied on the transmitter side, while classical coherent detection schemes are applied in both receivers. The joint monostatic-bistatic integrated EA transmitter is proposed suitable for implementation in LiNbO3 technology. The detection probability of the proposed EA joint target detection scheme outperforms significantly corresponding classical, coherent states-based quantum detection, and EA monostatic detection schemes. The proposed EA joint target detection scheme is evaluated by modelling the direct radar return and forward scattering channels as both lossy and noisy Bosonic channels, and assuming that the distribution of entanglement over idler channels is not perfect.

General Mixed-State Quantum Data Compression With and Without Entanglement Assistance

We consider the most general finite-dimensional quantum mechanical information source, which is given by a quantum system <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> that is correlated with a reference system <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> . The task is to compress <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> in such a way as to reproduce the joint source state <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho ^{AR}$ </tex-math></inline-formula> at the decoder with asymptotically high fidelity. This includes Schumacher’s original quantum source coding problem of a pure state ensemble and that of a single pure entangled state, as well as general mixed state ensembles. Here, we determine the optimal compression rate (in qubits per source system) in terms of the Koashi-Imoto decomposition of the source into a classical, a quantum, and a redundant part. The same decomposition yields the optimal rate in the presence of unlimited entanglement between compressor and decoder, and indeed the full region of feasible qubit-ebit rate pairs.

Constructions of &lt;i&gt;ℓ&lt;/i&gt;-Adic &lt;i&gt;t&lt;/i&gt;-Deletion-Correcting Quantum Codes

We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad. The second one corrects multiple deletions and can construct asymptotically good codes. The second one also allows conversion of stabilizer-based quantum codes to deletion-correcting codes, and entanglement assistance.

On entanglement assistance to a noiseless classical channel

For a classical channel, neither the Shannon ca-pa-city, nor the sum of conditional probabilities corresponding to the cases of successful transmission can be increased by the use of shared entanglement, or, more generally, a non-signaling resource. Yet, perhaps somewhat counterintuitively, entanglement assistance can help and actually elevate the chances of success even in a one-way communicational task that is to be completed by a single-shot use of a noiseless classical channel.To quantify the help that a non-signaling resource provides to a noiseless classical channel, one might ask how many extra letters should be added to the alphabet of the channel in order to perform equally well without the specified non-signaling resource. As was observed by Cubitt, Leung, Matthews, and Winter, there is no upper bound on the number of extra letters required for substituting the assistance of a general non-signaling resource to a noiseless one-bit classical channel. In contrast, here we prove that if this resource is a bipartite quantum system in a maximally entangled state, then an extra classical bit always suffices as a replacement.

Computable limits of optical multiple-access communications

Communication rates over quantum channels can be boosted by entanglement, via superadditivity phenomena or entanglement assistance. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses. Nevertheless, when unlimited entanglement assistance is available, the entanglement between channel uses becomes unnecessary -- the entanglement-assisted (EA) capacity of a single-sender and single-receiver channel is additive. We generalize the additivity of EA capacity to general multiple-access channels (MACs) for the total communication rate. Furthermore, for optical communication modelled as phase-insensitive bosonic Gaussian MACs, we prove that the optimal total rate is achieved by Gaussian entanglement and therefore can be efficiently evaluated. To benchmark entanglement's advantage, we propose computable outer bounds for the capacity region without entanglement assistance. Finally, we formulate an EA version of minimum entropy conjecture, which leads to the additivity of the capacity region of phase-insensitive bosonic Gaussian MACs if it is true. The computable limits confirm entanglement's boosts in optical multiple-access communications.

Entanglement Assisted Radars With Transmitter Side Optical Phase Conjugation and Classical Coherent Detection

Entanglement is a unique quantum information processing feature. With the help of entanglement we can build quantum sensors whose sensitivity is better than that of classical sensors. In this paper we are concerned with the entanglement assisted (EA) bistatic quantum radar applications. By employing the optical phase conjugation (OPC) on transmitter side and classical coherent detection on receiver side we show that the detection probability of the proposed EA target detection scheme is significantly better than that of corresponding classical and coherent states-based quantum detection schemes. The proposed EA target detection scheme is evaluated by modelling the radar return channel as the lossy and noisy Bosonic channel and assuming imperfect distribution of entanglement over the idler channel.

Modified quantum delayed-choice experiment without quantum control or entanglement assistance

Wheeler's delayed-choice experiment delays the decision to observe either the wave or particle behavior of a photon until after it has entered the interferometer, and the quantum delayed-choice experiment provides the possibility of observing the wave and particle behaviors with a single experimental setup by introducing quantum control. We here propose a modified quantum delayed-choice experiment without quantum control or entanglement assistance, in which a photon can be prepared in a wave-particle superposition state and the morphing behavior of wave-to-particle transition can be observed easily. It is demonstrated that the presented scheme can allow us to rule out classical hidden-variable models in a device-independent manner via violating dimension witness. We also extend the scheme to the situation of two degrees of freedom, first constructing a hybrid quantum delayed-choice experiment which enables a photon respectively exhibits wave and particle behaviors in different degrees of freedom, and then proposing a scheme to prepare the single-photon wave-particle entanglement. This study is not only meaningful to explore the wave-particle complementarity of photons, but also provides potential for the research of the single-particle nonlocality from the perspective of the wave-particle degree of freedom.

Quantum Receivers for Entanglement Assisted Classical Optical Communications

Entanglement assisted (EA) communication represents an interesting alternative to classical communication, in particular in low-brightness and highly noisy regime when it outperforms significantly corresponding classical counterpart in terms of the channel capacity. Even though that the EA capacity is known for decades the optimum quantum receiver has not been determined yet. In this paper, we propose several low-complexity quantum receivers outperforming recently proposed receivers employing the optical parametric amplifier as a basic building block. We demonstrate by simulations that the capacity of the proposed EA schemes, employing Gaussian modulation and the proposed low-complexity joint receivers, can significantly outperform both the Holevo capacity and classical homodyne and heterodyne channel capacities.

Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels

We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels (MACs) with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss MAC and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.

Two Families of Entanglement-Assisted Quantum MDS Codes from Cyclic Codes

With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of $q$-ary entanglement-assisted quantum MDS codes $[[\frac{q^{2}+1}{a},\frac{q^{2}+1}{a}-2(d-1)+c,d;c]]$, where q is a prime power in the form of $am+l$, and $a=(l^2+1)$ or $a=\frac{(l^2+1)}{5}$. We show that all of $q$-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.