Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States

We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops down discontinuously as soon as a nonzero error is tolerated and the spectrum of the states is known with sufficient precision. For qubit ensembles, this feature leads to a 25% saving of memory space. Our compression protocols can be implemented efficiently on a quantum computer.Comment: 5+19 pages, 2 figures. Published versio

Enhanced communication with the assistance of indefinite causal order

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, non-commuting processes, whose order (or lack thereof) can affect the ability to transmit information

Thermodynamics of quantum switch information capacity activation

We address a new setting where the second law is under question: thermalizations in a quantum superposition of causal orders, enacted by the so-called quantum switch. This superposition has been shown to be associated with an increase in the communication capacity of the channels, yielding an apparent violation of the data-processing inequality and a possibility to separate hot from cold. We analyze the thermodynamics of this information capacity increasing process. We show how the information capacity increase is compatible with thermodynamics. We show that there may indeed be an information capacity increase for consecutive thermalizations obeying the first and second laws of thermodynamics if these are placed in an indefinite order and moreover that only a significantly bounded increase is possible. The increase comes at the cost of consuming a thermodynamic resource, the free energy of coherence associated with the switch.Comment: 6+7pages,4 figure

General limit to thermodynamic annealing performance

Annealing has proven highly successful in finding minima in a cost landscape. Yet, depending on the landscape, systems often converge towards local minima rather than global ones. In this Letter, we analyse the conditions for which annealing is approximately successful in finite time. We connect annealing to stochastic thermodynamics to derive a general bound on the distance between the system state at the end of the annealing and the ground state of the landscape. This distance depends on the amount of state updates of the system and the accumulation of non-equilibrium energy, two protocol and energy landscape dependent quantities which we show are in a trade-off relation. We describe how to bound the two quantities both analytically and physically. This offers a general approach to assess the performance of annealing from accessible parameters, both for simulated and physical implementations.Comment: 6 pages, 3 figure

Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

Annealing is the process of gradually lowering the temperature of a system to guide it towards its lowest energy states. In an accompanying paper [Luo et al. Phys. Rev. E 108, L052105 (2023)], we derived a general bound on annealing performance by connecting annealing with stochastic thermodynamics tools, including a speed-limit on state transformation from entropy production. We here describe the derivation of the general bound in detail. In addition, we analyze the case of simulated annealing with Glauber dynamics in depth. We show how to bound the two case-specific quantities appearing in the bound, namely the activity, a measure of the number of microstate jumps, and the change in relative entropy between the state and the instantaneous thermal state, which is due to temperature variation. We exemplify the arguments by numerical simulations on the SK model of spin-glasses.Comment: 16 pages, 4 figure

Optimal universal quantum circuits for unitary complex conjugation

Let $U_d$ be a unitary operator representing an arbitrary $d$-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number $k$ of calls of $U_d$ into its complex conjugate $\bar{U_d}$. Our circuits admit a parallel implementation and are proven to be optimal for any $k$ and $d$ with an average fidelity of $\left\langle{F}\right\rangle =\frac{k+1}{d(d-k)}$. Optimality is shown for average fidelity, robustness to noise, and other standard figures of merit. This extends previous works which considered the scenario of a single call ($k=1$) of the operation $U_d$, and the special case of $k=d-1$ calls. We then show that our results encompass optimal transformations from $k$ calls of $U_d$ to $f(U_d)$ for any arbitrary homomorphism $f$ from the group of $d$-dimensional unitary operators to itself, since complex conjugation is the only non-trivial automorphisms on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.Comment: 19 pages, 5 figures. Improved presentation, typos corrected, and some proofs are now clearer. Closer to the published versio

Prospective randomized controlled clinical study comparing two types of two-piece dental implants supporting fixed reconstructions - results at 1 year of loading

OBJECTIVES To analyze clinical, esthetic, radiographic, and prosthetic outcomes of implants and implant-supported reconstructions using two types of dental implants with non-matching implant abutment junctions. MATERIALS AND METHODS A total of 64 patients in need of dental implant therapy with fixed reconstructions were consecutively enrolled. They were randomly assigned to either one of two implant systems (S1: Astra Tech Osseospeed and S2: Straumann Bone Level). Baseline (day of loading) and 1-year measurements included demographics, radiographic, clinical, biologic, prosthetic, and esthetic outcomes. All data were analyzed at the patient level and at the implant level. The nonparametric Mann-Whitney U-test was used to detect differences in continuous variables between two independent groups. RESULTS Ninety-seven implants (S1 = 54, S2 = 43) were placed and loaded with fixed reconstructions in 64 patients. No implant was lost during the 1-year observation period resulting in a 100% survival rate for both implant systems. At the patient level, the mean marginal bone level at implant insertion was -1.30 mm (SD ± 1.00 mm) for S1 and -1.26 mm (±1.22 mm) for S2 (negative values indicating bone levels coronal to the implant shoulder). At the time of loading, these distances measured 0.29 mm (±0.44 mm) for S1 and 0.22 mm (±0.43 mm) for S2. At the 1-year follow-up, these distances were 0.37 mm (±0.39 mm) for S1 and 0.39 mm (±1.02 mm) for S2. Technical complications of the reconstructions only occurred in Group S1, with a rate of 12% (patient level) (P > 0.05). Biologic complications were observed at a rate of 6% (S1) and 3.2% (S2) at the patient level (P > 0.05). CONCLUSIONS Both implant systems revealed 100% survival rates and minimal changes of the marginal bone levels during 1 year of loading. Few technical and biologic complications occurred. Therefore, both implant systems can be recommended for fixed reconstructions