Boosting Linear-Optical Bell Measurement Success Probability with Pre-Detection Squeezing and Imperfect Photon-Number-Resolving Detectors

Linear optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability $p_s$ no higher than $0.5$. However pre-detection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ${p_s \approx 0.643}$. The ability to achieve $p_s > 0.5$ has been found to be critical in resource-efficient realizations of linear optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of $p_s > 0.5$ is not known to be the maximum achievable using squeezing, thereby leaving it open whether close-to-$100\%$ efficient BSM might be achievable using squeezing as a resource. In this paper, we report new insights on why squeezing-enhanced BSM achieves $p_s > 0.5$. Using this, we show that the previously-reported ${p_s \approx 0.643}$ at single-mode squeezing strength $r=0.6585$---for unambiguous state discrimination (USD) of all four Bell states---is an experimentally unachievable point result, which drops to $p_s \approx 0.59$ with the slightest change in $r$. We however show that squeezing-induced boosting of $p_s$ with USD operation is still possible over a continuous range of $r$, with an experimentally achievable maximum occurring at $r=0.5774$, achieving ${p_s \approx 0.596}$. Finally, deviating from USD operation, we explore a trade-space between $p_s$, the probability with which the BSM circuit declares a "success", versus the probability of error $p_e$, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some $p_e > 0$, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with $p_s$ exceeding what is possible with traditionally-studied USD operation of BSMs.Comment: 13 pages, 10 figure

Non-producibility of arbitrary non-Gaussian states using zero-mean Gaussian states and partial photon number resolving detection

Gaussian states and measurements collectively are not powerful-enough resources for quantum computing, as any Gaussian dynamics can be simulated efficiently, classically. However, it is known that any one non-Gaussian resource -- either a state, a unitary operation, or a measurement -- together with Gaussian unitaries, makes for universal quantum resources. Photon number resolving (PNR) detection, a readily-realizable non-Gaussian measurement, has been a popular tool to try and engineer non-Gaussian states for universal quantum processing. In this paper, we consider PNR detection of a subset of the modes of a zero-mean pure multi-mode Gaussian state as a means to herald a target non-Gaussian state on the undetected modes. This is motivated from the ease of scalable preparation of Gaussian states that have zero mean, using squeezed vacuum and passive linear optics. We calculate upper bounds on the fidelity between the actual heralded state and the target state. We find that this fidelity upper bound is $1/2$ when the target state is a multi-mode coherent cat-basis cluster state, a resource sufficient for universal quantum computing. This proves that there exist non-Gaussian states that are not producible by this method. Our fidelity upper bound is a simple expression that depends only on the target state represented in the photon-number basis, which could be applied to other non-Gaussian states of interest.Comment: Revised version which now considers state engineering based on partial PNR detection, which subsumes subtraction and addition of photons. Said generalization allowed for cleaner and easier mathematical derivations. Appendix was taken from arXiv:2108.08290, co-authored by present authors and collaborators. Comments welcome and appreciate

Explicit receivers for pure-interference bosonic multiple access channels

The pure-interference bosonic multiple access channel has two senders and one receiver, such that the senders each communicate with multiple temporal modes of a single spatial mode of light. The channel mixes the input modes from the two users pairwise on a lossless beamsplitter, and the receiver has access to one of the two output ports. In prior work, Yen and Shapiro found the capacity region of this channel if encodings consist of coherent-state preparations. Here, we demonstrate how to achieve the coherent-state Yen-Shapiro region (for a range of parameters) using a sequential decoding strategy, and we show that our strategy outperforms the rate regions achievable using conventional receivers. Our receiver performs binary-outcome quantum measurements for every codeword pair in the senders' codebooks. A crucial component of this scheme is a non-destructive "vacuum-or-not" measurement that projects an n-symbol modulated codeword onto the n-fold vacuum state or its orthogonal complement, such that the post-measurement state is either the n-fold vacuum or has the vacuum removed from the support of the n symbols' joint quantum state. This receiver requires the additional ability to perform multimode optical phase-space displacements which are realizable using a beamsplitter and a laser.Comment: v1: 9 pages, 2 figures, submission to the 2012 International Symposium on Information Theory and its Applications (ISITA 2012), Honolulu, Hawaii, USA; v2: minor change

Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes

Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum convolutional codes are constructed from classical self-orthogonal \F_4-linear and \F_2-linear convolutional codes, respectively. These quantum convolutional codes have higher rate than comparable quantum block codes or previous quantum convolutional codes, and are simple to decode. A block single-error-correcting [9, 3, 3] tail-biting code is derived from the unrestricted convolutional code, and similarly a [15, 5, 3] CSS-type block code from the CSS-type convolutional code.Comment: 5 pages; to appear in Proceedings of 2005 IEEE International Symposium on Information Theor

Fundamental rate-loss tradeoff for optical quantum key distribution

Since 1984, various optical quantum key distribution (QKD) protocols have been proposed and examined. In all of them, the rate of secret key generation decays exponentially with distance. A natural and fundamental question is then whether there are yet-to-be discovered optical QKD protocols (without quantum repeaters) that could circumvent this rate-distance tradeoff. This paper provides a major step towards answering this question. We show that the secret-key-agreement capacity of a lossy and noisy optical channel assisted by unlimited two-way public classical communication is limited by an upper bound that is solely a function of the channel loss, regardless of how much optical power the protocol may use. Our result has major implications for understanding the secret-key-agreement capacity of optical channels---a long-standing open problem in optical quantum information theory---and strongly suggests a real need for quantum repeaters to perform QKD at high rates over long distances.Comment: 9+4 pages, 3 figures. arXiv admin note: text overlap with arXiv:1310.012

Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors

Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI)---a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCCassisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors.Comment: accepted for publication in Physical Review