Quantum illumination (QI) promises unprecedented performances in target detection but there are various problems surrounding its implementation. Where target ranging is a concern, signal and idler recombination forms a crucial barrier to the protocol's success. This could potentially be mitigated if performing a measurement on the idler mode could still yield a quantum advantage. In this paper we investigate the QI protocol for a generically correlated Gaussian source and study the phase-conjugating (PC) receiver, deriving the associated SNR in terms of the signal and idler energies, and their cross-correlations, which may be readily adapted to incorporate added noise due to Gaussian measurements. We confirm that a heterodyne measurement performed on the idler mode leads to a performance which asymptotically approaches that of a coherent state with homodyne detection. However, if the signal mode is affected by heterodyne but the idler mode is maintained clean, the performance asymptotically approaches that of the PC receiver without any added noise.
A quantum receiver is an essential element of quantum illumination (QI) which outperforms its classical counterpart, called classical-illumination (CI). However, there are only few proposals for realizable quantum receiver, which exploits nonlinear effects leading to increasing the complexity of receiver setups. To compensate this, in this article, we design a quantum receiver with linear optical elements for Gaussian QI. Rather than exploiting nonlinear effect, our receiver consists of a 50:50 beam splitter and homodyne detection. Using double homodyne detection after the 50:50 beam splitter,…
The signal half of an entangled twin-beam, generated using spontaneous parametric downconversion, interrogates a region of space that is suspected of containing a target, and has high loss and high (entanglement-breaking) background noise. A joint measurement is performed on the returned light and the idler beam that was retained at the transmitter. An optimal quantum receiver, whose implementation is not yet known, was shown to achieve 6 dB gain in the error-probability exponent relative to that achieved with a single coherent-state (classical) laser transmitter and the optimum receiver. We p…
In quantum illumination, the signal mode of light, entangled with an idler mode, is dispatched towards a suspected object bathed in thermal noise and the returning mode, along with the stored idler mode, is measured to determine the presence or absence of the object. In this process, entanglement is destroyed but its benefits in the form of classical correlations and enlarged Hilbert space survive. Here, we propose the use of probe state hyperentangled in two degrees of freedom - polarization and frequency, to achieve a significant 12dB performance improvement in error probability exponent ove…
We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The observable bounds are achieved with mode-by-mode measurements. In the quantum regime using a two-mode squeezed vacuum state, our observable receiver outperforms the other feasible receivers whereas it cannot approach the quantum Chernoff bound. The corresponding observable cannot be implemented with heterodyne detections due to the additional vacuum noise. In the classical …
An optical transmitter that uses entangled light generated by spontaneous parametric downconversion (SPDC), in conjunction with an optimal quantum-optical receiver (whose implementation is not yet known) is in principle capable of obtaining up to a 6 dB gain in the error-probability exponent over the optimum-reception un-entangled coherent-state lidar to detect the presence of a far-away target subject to entanglement-breaking loss and noise in the free-space link [Lloyd'08, Tan'08]. We present an explicit design of a structured quantum-illumination receiver, which in conjunction with the SPDC…
We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state…
We propose Gaussian quantum illumination(QI) protocol exploiting asymmetrically squeezed two-mode(ASTM) state that is generated by applying single-mode squeezing operations on each mode of an initial two-mode squeezed vacuum(TMSV) state, in order to overcome the limited brightness of a TMSV state. We show that the performance of the optimal receiver is enhanced by local squeezing operation on a signal mode whereas the performance of a realistic receiver can be enhanced by local squeezing operations on both input modes. Under a fixed mean photon number of the signal mode, the ASTM state can be …
Quantum illumination is a powerful sensing technique that employs entangled signal-idler photon pairs to boost the detection efficiency of low-reflectivity objects in environments with bright thermal noise. The promised advantage over classical strategies is particularly evident at low signal powers, a feature which could make the protocol an ideal prototype for non-invasive biomedical scanning or low-power short-range radar. In this work we experimentally investigate the concept of quantum illumination at microwave frequencies. We generate entangled fields using a Josephson parametric convert…
This research note II introduces a way to understand a basic concept of the quantum enigma cipher. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm in security analysis and ability of computers. This kind of cipher can be decrypted with probability one in principle by the Brute force attack in which an eavesdropper tries all the possible keys based on the correct ciphertext and some known plaintext. A cipher with quantum effects in physical layer may protect the system from the Brute force attack by means of the qu…
Loss and noise quickly destroy quantum entanglement. Nevertheless, recent work has shown that a quadrature-entangled light source can reap a substantial performance advantage over all classical-state sources of the same average transmitter power in scenarios whose loss and noise makes them entanglement breaking, standoff target-detection being an example. In this paper, we make a first step in extending this quantum illumination paradigm to the optical imaging domain, viz., to obtain better spatial resolution for standoff optical sensing. Our canonical imaging scenario---restricted, for simpli…
Lloyd [1] proved that a large performance gain accrues from use of entanglement in single-photon target detection within a lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We show that the performance of Lloyd's "quantum illumination" system is, at best, equal to that of a coherent-state transmitter, and may be substantially worse. Nevertheless, as shown in [2], quantum illumination may offer a significant performance gain when operation is not limited to the single-photon regime.
Quantum-enhanced sensing has a goal of enhancing a parameter sensitivity with input quantum states, while quantum illumination has a goal of enhancing a target detection capability with input entangled states in a heavy noise environment. Here we propose a concatenation between quantum-enhanced sensing and quantum illumination that can take quantum advantage over the classical limit. First, phase sensing in an interferometry is connected to a target sensing via quantum Fisher information. Second, the target sensitivity is investigated in noisy quantum-enhanced sensing. Under the same input sta…
Quantum illumination is the task of determining the presence of an object in a noisy environment. We determine the optimal continuous variable states for quantum illumination in the limit of zero object reflectivity. We prove that the optimal single mode state is a coherent state, while the optimal two mode state is the two-mode squeezed-vacuum state. We find that these probes are not optimal at non-zero reflectivity, but remain near optimal. This demonstrates the viability of the continuous variable platform for an experimentally accessible, near optimal quantum illumination implementation.
We consider the problem of trying to send a single classical bit through a noisy quantum channel when two transmissions through the channel are available as a resource. Classically, two transmissions add nothing to the receiver's capability of inferring the bit. In the quantum world, however, one has the possible further advantage of entangling the two transmissions. We demonstrate that, for certain noisy channels, such entangled transmissions enhance the receiver's capability of a correct inference.
We consider the problem of estimating unknown transmittance $θ$ of a target bathed in thermal background light. As quantum estimation theory yields the fundamental limits, we employ the lossy thermal-noise bosonic channel model, which describes sensor-target interaction quantum mechanically in many practical active-illumination systems (e.g., using emissions at optical, microwave, or radio frequencies). We prove that quantum illumination using two-mode squeezed vacuum (TMSV) states asymptotically achieves minimal quantum Cramér-Rao bound (CRB) over all quantum states (not necessarily Gaussian)…
Quantum illumination (QI) provides entanglement-based target detection---in an entanglement-breaking environment---whose performance is significantly better than that of optimum classical-illumination target detection. QI's performance advantage was established in a Bayesian setting with the target presumed equally likely to be absent or present and error probability employed as the performance metric. Radar theory, however, eschews that Bayesian approach, preferring the Neyman-Pearson performance criterion to avoid the difficulties of accurately assigning prior probabilities to target absence…
The benefits of entanglement can outlast entanglement itself. In quantum illumination, entanglement is employed to better detect reflecting objects in environments so noisy that all entanglement is destroyed. Here, we show that quantum discord - a more resilient form of quantum correlations - explains the resilience of quantum illumination. We introduce a quantitative relation between the performance gain in quantum illumination and the amount of discord used to encode information about the presence or absence of a reflecting object. This highlights discord's role preserving the benefits of en…
We have tried to interpret the physical role of the three-tangle and $π$-tangle in the real physical information process. For the model calculation we adopt the three-party teleportation scheme through the various noisy channels. The three parties consist of sender, accomplice and receiver. It is shown that the $π$-tangles for the X- and Z-noisy channels vanish at $κt \to \infty$ limit, where $κt$ is a parameter introduced in the master equation of Lindblad form. In this limit the receiver's maximum fidelity reduces to the classical limit 2/3. However, this nice feature is not maintained at th…
Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources, and thus nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise.…
Quantum illumination (QI) is an entanglement-enhanced sensing system whose performance advantage over a comparable classical system survives its usage in an entanglement-breaking scenario plagued by loss and noise. In particular, QI's error-probability exponent for discriminating between equally-likely hypotheses of target absence or presence is 6 dB higher than that of the optimum classical system using the same transmitted power. This performance advantage, however, presumes that the target return, when present, has known amplitude and phase, a situation that seldom occurs in lidar applicati…
Quantum communication is one of the cutting-edge research areas today, where the scheme of Remote State Preparation (RSP) has caught significant attention of researchers. A number of different schemes of RSP have already been proposed so far. We propose here a hierarchical RSP protocol for sending a two-qubit entangled state using a seven-qubit highly entangled state derived from Brown et al. state. We have also studied here the effects of two well known noise models namely amplitude damping (AD) and phase damping (PD) that affect the quantum communication channel used for the protocol. An inv…
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated codewords with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations…
Suppose that $m$ senders want to transmit classical information to $n$ receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each $m$ and $n$ with $m\ge 2$ or $n\ge 2$, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and i…
Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illuminat…
Quantum illumination (QI) is a quantum sensing protocol mainly for target detection which uses entangled signal-idler photon pairs to enhance the detection efficiency of low-reflectivity objects immersed in thermal noisy environments. Especially, due to the naturally occurring background radiation, the photon emitted toward potential targets more appropriately lies in the microwave region. Here, we propose a hybrid quantum source based on cavity magnonics for microwave QI, where the medium that bridges the optical and the microwave modes is magnon, the quanta of spin wave. Within experimentall…
Quantum key distribution can be enhanced and extended if nonclassical single-photon states of light are used. We study a connection between the security of quantum key distribution and quantum non-Gaussianity of light arriving at the receiver's detection system after the propagation through a noisy quantum channel, being under full control of an eavesdropper performing general collective attacks. We show that while quantum nonclassicality exhibited by the light arriving at the receiver's station is a necessary indication of the security of the discrete-variable protocols, quantum non-Gaussiani…
Quantum illumination (QI) theoretically promises up to a 6dB error-exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime which includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well-known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally us…
With the aim to loosen the entanglement requirements of quantum illumination, we study the performance of a family of Gaussian states at the transmitter, combined with an optimal and joint quantum measurement at the receiver. We find that maximal entanglement is not strictly necessary to achieve quantum advantage over the classical benchmark of a coherent-state transmitter, in both settings of symmetric and asymmetric hypothesis testing. While performing this quantum-classical comparison, we also investigate a suitable regime of parameters for potential short-range radar (or scanner) applicati…
We cast the problem of illuminating an object in a noisy environment into a communication protocol. A probe is sent into the environment, and the presence or absence of the object constitutes a signal encoded on the probe. The probe is then measured to decode the signal. We calculate the Holevo information and bounds to the accessible information between the encoded and received signal with two different Gaussian probes---an Einstein-Podolsky-Rosen (EPR) state and a coherent state. We also evaluate the Gaussian discord consumed during the encoding process with the EPR probe. We find that the H…
By harnessing the quantum states of light for illumination, precise phase and absorption estimations can be achieved with precision beyond the standard quantum limit. Despite their significance for precision measurements, quantum states are fragile in noisy environments which leads to difficulties in revealing the quantum advantage. In this work, we propose a scheme to improve optical absorption estimation precision by using the correlated photon pairs from spontaneous parametric down-conversion as the illumination. This scheme performs better than clasical illumination when the loss is below …
A new paradigm for secure communication, based on quantum illumination, is proposed. Alice uses spontaneous parametric down-conversion to send Bob a set of signal modes over a pure-loss channel while retaining the set of idler modes with which they are maximally entangled. Bob imposes a single information bit on the modes he receives from Alice via binary phase-shift keying. He then adds classical Gaussian noise and sends the noisy modulated modes back to Alice over the same pure-loss channel. Even though the loss and noise destroy any entanglement between the modes that Alice receives from Bo…
Quantum target detection is an emerging application that utilizes entanglement to enhance the sensing of the presence of an object. Although several experimental demonstrations for certain situations have been reported recently, the single-shot detection limit imposed by the Helstrom limit has not been reached because of the unknown optimum measurements. Here we report an experimental demonstration of quantum target detection, also known as quantum illumination, in the single-photon limit. In our experiment, one photon of the maximally entangled photon pair is employed as the probe signal and …
Quantum illumination consists in shining quantum light on a target region immersed in a bright thermal bath, with the aim of detecting the presence of a possible low-reflective object. If the signal is entangled with the receiver, then a suitable choice of the measurement offers a gain with respect to the optimal classical protocol employing coherent states. Here, we tackle this detection problem by using quantum estimation techniques to measure the reflectivity parameter of the object, showing an enhancement in the signal-to-noise ratio up to 3 dB with respect to the classical case when imple…
Quantum illumination can utilize entangled light to detect the low-reflectivity target that is hidden in a bright thermal background. This technique is applied to the detection of an object in the curved spacetime of the Earth, in order to explore how the curvature of spacetime affects quantum illumination. It is found that the spatial quantum illumination with entangled state transmitter outperforms that with coherent-state transmitter in the near-Earth curved spacetime. Moreover, either the quantum illumination system or the coherent-state system is employed, and gravity can enhance the spac…
In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback from receiver to sender. In this paper the use of classical feedback is shown to provide no increase in the unassisted classical capacity of a memoryless quantum channel when feedback is used across non-entangled input states, or when the channel is an entanglement--breaking channel. This gives a generalization of the Shannon theory for certain classes of feedback protocols when transmitting through noisy quantum communication channels.
This paper proposes a multi-mode Gaussian modulated continuous variable quantum key distribution (CV-QKD) scheme able to operate at high bandwidth despite using conventional noisy, coherent detectors. We demonstrate enhancement in shotnoise sensitivity as well as reduction in the electronic noise variance of the coherent receiver of the multi-mode CV-QKD system. A proof-of-concept simulation is presented using multiple modes; this demonstrates an increase in signal-to-noise ratio and secure key rate at various transmission distances with increasing signal modes.
In Quantum Illumination (QI), a signal beam initially entangled with an idler beam held at the receiver interrogates a target region bathed in thermal background light. The returned beam is measured jointly with the idler in order to determine whether a weakly reflecting target is present. Using tools from quantum information theory, we derive lower bounds on the average error probability of detecting both specular and fading targets and on the mean squared error of estimating the reflectance of a detected target, which are obeyed by any QI transmitter satisfying a signal energy constraint. Fo…
We study the performance of the super dense coding protocol in the presence of quantum channels with covariant noise. We first consider the bipartite case and review in a unified way the case of general Pauli channels. We discuss both the cases of unitary and non-unitary encoding. We also study the multipartite scenario and investigate the case of many senders and one receiver.
Quantum teleportation enables deterministic and faithful transmission of quantum states, provided a maximally entangled state is pre-shared between sender and receiver, and a one-way classical channel is available. Here, we prove that these resources are not only sufficient, but also necessary, for deterministically and faithfully sending quantum states through any fixed noisy channel of maximal rank, when a single use of the cannel is admitted. In other words, for this family of channels, there are no other protocols, based on different (and possibly cheaper) sets of resources, capable of rep…
Sender and receiver can control noisy channels by means of the resources they own, that is local operations, potentially correlated using classical communication, and entangled pairs shared between them. Using the Choi-Jamiolkowski isomorphism, we express the control of a noisy channel in terms of control of (non-normalized) states, and show how the available resources enter the analysis. Our formalism provides a general scheme for the protection of quantum state transmission when a single use of the physical channel is considered. Moreover, it paves the way to the application of control theor…
A novel scheme for quantum communication having substantial applications in practical life is designed and analyzed. Specifically, we have proposed a hierarchical counterpart of the joint remote state preparation (JRSP) protocol, where two senders can jointly and remotely prepare a quantum state. One sender has the information regarding amplitude, while the other one has the phase information of a quantum state to be jointly prepared at the receiver's port. However, there exists a hierarchy among the receivers, as far as powers to reconstruct the quantum state is concerned. A 5-qubit cluster s…
