arXiv subjects

Piotr Ćwikliński

Publications and source records attributed to Piotr Ćwikliński.

14 recordsLinked to original sources

arXiv2026

Finite-time quantum equilibration from local correlations

An isolated quantum system evolves reversibly, yet a small subsystem can lose nearly all information about its initial state. Conserved quantities may retain some of this information, depending on how strongly they overlap with local observables. Here we consider a subsystem in an arbitrary initial state coupled to a maximally mixed bath. We show that the worst-input mean-square equilibration error, maximised over window origins, is bounded from above and below by the mean square of a complete local autocorrelation, with the stationary part subtracted. A correlation record over a finite interval therefore controls the equilibration error in every interval of the same length. The result allows arbitrary degeneracies of energies and gaps. We apply it to two static Hamiltonian families. For fixed spin subsystems in the one-particle sector of a bounded-range periodic clock, fixed-accuracy thermalisation is guaranteed on windows that grow only slightly faster than linearly with system size, despite exponentially small positive energies. A random commuting model with logarithmic interaction range retains an extensive set of conserved observables. Its expected mean-square error is bounded by a finite-size term and an inverse-time term. The inverse-time dependence is unavoidable because of the initial transient. These examples show how local relaxation can coexist with exact conservation laws and a finely spaced spectrum.

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arXiv2026

Asymmetric quantum cloning on orthogonal orbits and four-mode fermionic states

In this work, we study asymmetric $(1\to2)$ quantum cloning for pure states belonging to orbits generated by the orthogonal group. For every dimension $(d\geq3)$, we determine the full region of achievable pairs of average single-copy fidelities. Using orthogonal covariance and the Brauer algebra, we reduce the optimization over all CPTP maps to a finite-dimensional spectral problem and construct explicit optimal cloning channels. We then apply the general results to four-mode fermionic states in the even-parity sector. Using triality, we identify the fixed-concurrence fermionic families with the orthogonal orbits considered in the first part of the paper. In particular, for pure Gaussian states we show that the symmetric locally optimal cloner is unique. We also compare local and global cloning and find that the channel optimal for the joint two-copy fidelity is different from the one optimal for the single-copy fidelities. Finally, we show that the locally optimal cloner cannot be implemented using only operations which preserve fermionic Gaussian states.

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arXiv2026

Limitations on Joint Coherence Transfer in Quantum Thermodynamics

Coherences between different energy levels are strongly constrained by thermodynamics. Here we ask a related question: if several coherence transfers can be optimized separately, can they also be optimized simultaneously by the same thermodynamic process? We show that this is in general a compatibility problem. Using an energy-resolved Stinespring representation of thermal operations, we express elementary coherence-transfer amplitudes as inner products of bath-weighted vectors associated with total-energy shells. Saturation of the corresponding Cauchy--Schwarz bounds requires these vectors to be collinear. Since all transfers have to arise from the same energy-preserving system--bath unitary, such saturation conditions cannot in general be imposed independently. Trace and Gibbs preservation lead to additional phase-closure conditions and to polygon inequalities that can rule out simultaneous saturation for fixed population-transfer data. We complement these analytic results with a rigorous computer-assisted semidefinite-program analysis. For the mixed-degenerate Hamiltonian $H=\operatorname{diag}(0,1,1,3)$, machine-certified primal and dual bounds show that no covariant Gibbs-preserving channel can simultaneously attain three individually optimal directional coherence transfers. Since every thermal operation is covariant and Gibbs preserving, the same triple of $\CGP$-optimal values cannot be attained by a thermal operation. We also analyze auxiliary Choi-sector Gram matrices for mixed-degenerate ladders. Under specified directional rank assumptions, positivity imposes range-inclusion conditions, from which we obtain conditional non-genericity statements for physical joint saturation.

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arXiv2026

Thermodynamic Value of XOR-Game-Induced Side Information in a Szilard Engine

In this work, we study the reversible work value of a binary side-information channel supplied to a Szilard engine. The working system is a classical thermal bit, while the feedback controller receives only a binary record correlated with its physical state. We show that a fixed average prediction accuracy does not determine a unique thermodynamic value, because different binary channels with the same accuracy can carry different amounts of mutual information. We derive the exact minimum and maximum reversible Szilard work compatible with a given prediction accuracy. The minimum is attained uniquely by the binary symmetric channel, whereas the maximum is attained by two asymmetric channels for which all errors are concentrated on one input value. We then show that the standard XOR-game embedding always produces the symmetric channel and therefore realizes the minimum possible Szilard work among all binary side-information channels with the same prediction accuracy. Finally, we contrast this information-to-work valuation with an event-routing battery valuation, which depends only on the task-success probability.

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arXiv2026

Battery-Explicit Thermodynamic Witnesses of Bell Post-Quantumness

We introduce a battery-explicit thermodynamic witness of post-quantum Bell correlations. In each round, a single supplied excitation is routed into an explicit two-level battery if and only if a Bell-game condition is satisfied. The routing operation is implemented by an energy-preserving controlled SWAP, with all logical control registers taken to be degenerate. Thus the correlation resource does not create energy; it only determines the probability that the supplied excitation reaches the battery. The construction is first formulated for finite two-player XOR games. For any such game, the mean battery charge is exactly the game success probability multiplied by the battery gap. Optimizing over local, quantum, or nonsignalling behaviours therefore turns the corresponding game values into local, quantum, or nonsignalling battery-charge ceilings. For the CHSH game, Tsirelson's bound becomes a strict quantum ceiling on the mean battery charge, while a PR-box behaviour reaches the single-excitation cap. The witness is trusted-module rather than device-independent: it assumes calibrated Hamiltonians, correct classical wiring, and a trusted energy-preserving battery module. We also discuss a reversible-controller implementation, finite-statistics certification from work data, robustness to imperfect battery readout, and cyclic bookkeeping showing that no positive net work is obtained once fuel restoration and memory erasure are included.

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arXiv2026

Thermal Operations in general are not memoryless

So-called Thermal Operations seem to describe the most fundamental and reasonable set of operations allowable for state transformations at an ambient inverse temperature $β$. However, a priori, they require experimentalists to manipulate very complex environments and have control over their internal degrees of freedom. For this reason, the community has been working on creating more experimentally-friendly operations. In [Perry, et al., Phys. Rev. X 8, 041049], it was shown that for states diagonal in the energy basis, Thermal Operations can be performed by so-called Coarse Operations, which need just one auxiliary qubit but are otherwise Markovian and classical in spirit. In this work, by providing an explicit counterexample, we show that this one qubit of memory is necessary. We also provide almost full characterization (i.e., full, but with one intriguing exception that remains open) of possible transitions that do not require memory in the case where the system is a qubit. We do this by analyzing arbitrary control sequences comprising level energy changes and partial thermalizations in each step.

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arXiv2016

A sufficient set of experimentally implementable thermal operations

Recent work using tools from quantum information theory has shown that at the nanoscale where quantum effects become prevalent, there is not one thermodynamical second law but many. Derivations of these laws assume that an experimenter has very precise control of the system and heat bath. Here we show that these multitude of laws can be saturated using two very simple operations: changing the energy levels of the system and thermalizing over any two system energy levels. Using these two operations, one can distill the optimal amount of work from a system, as well as perform the reverse formation process. Even more surprisingly, using only these two operations and one ancilla qubit in a thermal state, one can transform any state into any other state allowable by the second laws. We thus have the remarkable result that the second laws hold for fine-grained manipulation of system and bath, but can be achieved using very coarse control. This brings the full array of thermal operations into a regime accessible by experiment, and establishes the physical relevance of these second laws.

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arXiv2015

Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences

The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into another if the free energy goes down. Recently, it's been shown that there are actually many second laws, and that it is only for large macroscopic systems that they all become equivalent to the ordinary one. These additional second laws also hold for quantum systems, and are, in fact, often more relevant in this regime. They place a restriction on how the probabilities of energy levels can evolve. Here, we consider additional restrictions on how the coherences between energy levels can evolve. Coherences can only go down, and we provide a set of restrictions which limit the extent to which they can be maintained. We find that coherences over energy levels must decay at rates that are suitably adapted to the transition rates between energy levels. We show that the limitations are matched in the case of a single qubit, in which case we obtain the full characterization of state-to-state transformations. For higher dimensions, we conjecture that more severe constraints exist. We also introduce a new class of thermodynamical operations which allow for greater manipulation of coherences and study its power with respect to a class of operations known as thermal operations.

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arXiv2015

Construction and properties of a class of private states in arbitrary dimensions

We present a construction of quantum states in dimension $d$ that has at least 1 dit of ideal key, called private dits (pdits), which covers most of the known examples of private bits (pbits) $d=2$. We examine properties of this class of states, focusing mostly on its distance to the set of separable states $\mathcal{SEP}$, showing that for a fixed dimension of key part $d_k$ the distance increases with $d_s$. We provide explicit examples of PPT states (in $d$ dimensions) which are nearly as far from separable ones as possible. Precisely, the distance from the set of $\mathcal{SEP}$ is $2 - ε$, where $d$ scales with $ε$ as $d \propto 1/ε^3$, as opposed to $d \propto 2^{(log(4/ε))^2}$ obtained in [Badzicag et al., Phys. Rev. A 90, 012301 (2014)]. We do not use boosting (taking many copies of pdits to boost the distance) as in Badzicag et al. paper.

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arXiv2014

Group representation approach to 1 - N universal quantum cloning machines

In this work, we revisit the problem of finding an admissible region of fidelities obtained after an application of an arbitrary $1 \rightarrow N$ universal quantum cloner which has been recently solved in [A. Kay et al., Quant. Inf. Comput 13, 880 (2013)] from the side of cloning machines. Using group-theory formalism, we show that the allowed region for fidelities can be alternatively expressed in terms of overlaps of pure states with recently found irreducible representations of the commutant $U \otimes U \otimes \ldots \otimes U \otimes U^*$, which gives the characterization of the allowed region where states being cloned are figure of merit. Additionally, it is sufficient to take pure states with real coefficients only, which makes calculations simpler. To obtain the allowed region, we make a convex hull of possible ranges of fidelities related to a given irrep. Subsequently, two cases: $1 \rightarrow 2$ and $1 \rightarrow 3$ cloners, are studied for different dimensions of states as illustrative examples.

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arXiv2013

Local random quantum circuits are approximate polynomial-designs - numerical results

We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al., arXiv:1208.0692]. Using a group theory formalism, spectral gaps that give a ratio of convergence to a given t-design are evaluated for a different number of qubits n (up to 20) and degrees t (t=2,3,4 and 5), improving previously known results for n=2 in the case of t=2 and 3. Their values lead to a conclusion that the previously used lower bound that bounds spectral gaps values may give very little information about the real situation and in most cases, only tells that a gap is closed. We compare our results to the another lower bounding technique, again showing that its results may not be tight.

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arXiv2013

The Power of Noisy Fermionic Quantum Computation

We consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi [Phys. Rev. A 73, 042313 (2006)] that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular 4-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated classically: we explicitly show that the noisy ancilla is a convex mixture of Gaussian fermionic states in this region, while for noise rates below 53% we prove that the state is not a mixture of Gaussian states. These results were obtained by generalizing concepts in entanglement theory to the setting of Gaussian states and their convex mixtures. In particular we develop a complete set of criteria, namely the existence of a Gaussian-symmetric extension, which determine whether a state is a convex mixture of Gaussian states.

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arXiv2012

Convergence to equilibrium under a random Hamiltonian

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

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arXiv2012

Region of fidelities for a 1 -> N universal qubit quantum cloner

We analyze a region of fidelities for qubit which is obtained after an application of a 1 -> N universal quantum cloner. We express the allowed region for fidelities in terms of overlaps of pure states with irreps of S(n) (n = N+1) showing that the pure states can be taken with real coefficients only. Subsequently, the case n = 4, corresponding to a 1 -> 3 cloner is studied in more detail as an illustrative example. To obtain the main result, we make a convex hull of possible ranges of fidelities related to a given irrep. The formalism allows to construct the state giving rise to a given N-tuple of fidelities.

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